Product Description
Clarity, readability and rigor combine in the second edition of this widely-used textbook to provide the first step into general relativity for undergraduate students with a minimal background in mathematics. Topics within relativity that fascinate astrophysical researchers and students alike are covered with Schutz's characteristic ease and authority - from black holes to gravitational lenses, from pulsars to the study of the Universe as a whole. This edition now contains discoveries by astronomers that require general relativity for their explanation; a revised chapter on relativistic stars, including new information on pulsars; an entirely rewritten chapter on cosmology; and an extended, comprehensive treatment of modern detectors and expected sources. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, whilst the informal writing style makes the subject matter easily accessible. ... Read more

Customer Reviews (26)

Excellent book for REALLY getting in to GR
Schultz's book was recommended in Sean Carroll's on-line physics notes.It is terrific for someone who has a good grasp of Special Relativity but needs some hand holding in General Relativity.I think I am actually grasping the ideas mathematically for the first time.

Good introduction
This books spends a good amount on the basic math and introduction to tensors.You don't need much background to make your way through the material.It provides a nice set of exercises to reinforce the concepts presented in the text.

good first book for learning general relativity
This book is a good introduction to relativity which does not pull punches mathematically speaking but still manages to be merciful to the beginner. I read this book with only a basic background in freshman college physics and calculus. It took me 2 6-month sessions over 2 years to go through it all in detail but it was worth it. It gave me a sufficient familiarity with the core concepts and underlying mathematics to consider tackling a more advanced book on relativity someday. The book starts with special relativity, Minkowski diagrams, 4-vectors, etc., then progresses through background material on tensors, one-forms, metrics, etc. It then goes over general covariance, geodesics in curved spacetime, and the equations of general relativity. Following this there is material on the weak gravity (Newtonian) approximation, including the derivation of the precession of Mercury, a key confirmation of Einstein's theory. Then various metrics relevant to cosmology and black holes are discussed, including the Friedmann-Lemaitre metric (the expanding universe), and the Kerr metric (rotating black holes). It was quite fascinating to see the actual mathematical derivations of many of the key concepts and findings of general relativity that I had previously only read about in popular science books. Each chapter comes with problems which help illuminate the material.

A very worthwhile exercise if non-mathematical descriptions of relativity, cosmology, and high-energy astrophysics leave you wishing for a more in-depth understanding, and if you have a basic physics and math background and the time to spend. Five stars!

As easy as it can be
Nice introduction to GR. Not extensive previous knowledge needed and as clear as it could be.

As the title says, a good 'First Course'
There are a lot of books on General Relativity. In approach they vary from no math, to essentially math books. This book is somewhere in the middle. It is said to be suitable for a one year course for beginning graduate students or for undergraduates in physics who have studied special relativity, vector calculus, and electrostatics.

To enable such a student to follow the math in in this book the first part of the book reviews special relativity and vector analysis. Then the book has a section on Tensor Analysis, which was newly developed in Einstein's time when it was called tensor calculus. The treatment of these mathematical concepts in this book are, in my mind, sufficient for a review for a student that had studied them before, but will require some pretty good insight for a student that had not seen them before. This background information covers about a third of the book.

Chapter 5 of the book starts out, 'Until now we have discussed only SR.' The next two thirds cover curvature, physics in a curved spacetime, the Einstein field equations, gravitational radiation (the biggest chapter in the book), and on to the rest of GR.

By the end of the book the student has indeed completed a 'first course' in GR. There is still plenty more to go for the interested student specializing in this area. ... Read more

Product Description
THE PRESENT book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus 1 of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation examination, and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader. The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated. In the interest of clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation. I adhered scrupulously to the precept of that brilliant theoretical physicist, L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and to the cobbler. I make no pretence of having with-held from the reader difficulties which are inherent to the subject. On the other hand, I have purposely treated the empirical physical foundations of the theory in a ?step-motherly? fashion, so that readers unfamiliar with physics may not feel like the wanderer who was unable to see the forest for trees. May the book bring some one a few happy hours of suggestive thought!

Table of Contents

Part I: The Special Theory of Relativity
1. Physical Meaning of Geometrical Propositions
2. The System of Co-ordinates
3. Space and Time in Classical Mechanics
4. The Galileian System of Co-ordinates
5. The Principle of Relativity (In the Restricted Sense)
6. The TheoAmazon.com Review
How better to learn the Special Theory of Relativity and theGeneral Theory of Relativity than directly from their creator, AlbertEinstein himself? In Relativity: The Special and the GeneralTheory, Einstein describes the theories that made him famous,illuminating his case with numerous examples and a smattering of math(nothing more complex than high-school algebra). Einstein's book isnot casual reading, but for those who appreciate his work withoutdiving into the arcana of theoretical physics, Relativity willprove a stimulating read. ... Read more

Customer Reviews (87)

The Best Way to Discredit Any Work

Before buying looked for reviews.There are49 out of 86 five star ones. So opted to buyto get a chance to touch the work of a genius. Never happened though.The book begins with text references to Fig. 1, Fig 2, Fig. 3, etc.No such diagrams.....Nada, just empty spaces... As a matter of fact, not a single drawing in the book! I mean, the book is reprinted with NO crucial accompanying the text drawings. Probably, the latter were in a separate file which they didn't copyright to make it cheaper, anyway it rendered the book useless. I would've sentenced the editor to a jail time.
Ah, here it is: "We recreated the book from the original using Optical Character Recognition to keep the cost of the book as low as possible. Therefore could you please forgive...etc. "
Yup, they sure hit the jackpot! Actually it's a fraud. At "Look Inside"they show you another edition!
In hindsight I suspect some 5-4 star reviews are fictitious(if not most of them)...OR they combined all reviews from different publications into one file. Buyer be aware!
Joseph Zacharow.

This edition created by OCR, many errors!
This edition of Einstein's wonderful book was, according to the publisher, "...recreated from the original using Optical Character Recognition software to keep the cost of the book as low as possible. Therefore, could you please forgive any spelling mistakes, missing or extraneous characters that may have resulted..."

It's obvious that the publisher didn't bother to proof read the result of the OCR scan. There are many errors throughout the book. Some are obvious, others make it hard to read, or understand what the original text said. Here's an example from Section 2:

m
SPACE AND TIME IN CLASSICAL MECHANICS
"rTTHE purpose of mechanics is to describe how I bodies change their position in space with time."

Another example from section 3, which shows an incorrect formula: W = C | V.
It is supposed to read: w = c-v

Footnotes are jumbled, and references to the footnotes are left out.

The edition is readable, thus two stars. But the poor or non-existant editing makes it harder. Avoid this edition and get one where you don't trip over all the errors introduced by OCR.

be careful which copy you buy
Do not buy the copy of this book with ISBN 978-1452841212 !!! You have been warned! The equations which are set out as images (ie any that require more than simple typesetting) have not been printed, and the text just shows the file name instead eg. eq1.gif. I can't believe that they're selling this book! The other copies are ok from what I have seen on the preview pages.

Great book - Kindle edition readablity needs work (Driod only?)
Caveat - The equations are written in a very small font and thus on the kindle edition are next to impossible to read.I should indicate that I'm reading on a Driod.Thus, readers using other viewers might not have a problem.If it were possible to zoom into the equations, this would not be an issue, but as far as I can tell on the driod you can't zoom in.

Relativity Explained by the Master Himself
Professor Einstein wrote this book for the general audience who had an education "comparable to that of a university matriculation examination", as he felt there was a great need of introducing the idea to the public; however, the original papers were too technical. He did warn that reading the book would require the reader to exert some effort, and I certainly did. However, I derived some solace from the fact that out of all the books on relativity in the (university) library, this book is one of the few that is comprehensible to me!

He first sets out conventional thinking of the day on relative motion and invites us to consider the "truth" carefully. He reviewed the concept of reference frame (i.e. coordinate system) and the use of Euclidean geometry to describe relative motion, including the 'intuitive' addition of velocity. Then he reveals that this line of thought is problematic.

At this point it is worth digressing into the means which he presents the theory of relativity. His presentation is elegant - not in the linguistic sense, but in the structure of his argument. Normally, one can start with a set of empirical data and try to work out a pattern, from there on, a theory. One can also formulate questions, let imagination and reasoning suggest a hypothesis, then find experimental data to test the hypothesis.

Einstein did it another way still, at least in this book. His general pattern is to explore some thought experiments and to see their implications. From there, he formulates the postulates and work out a coherent theory from the postulates. Experiments only come much later in his style of presentation. In particular, he postulates that (i) the speed of light is constant for all observers and (ii) physical laws are the same for observers in all reference frames. He then conducts a thought experiment, the now-famous train/lightning experiment. The two lightning bolts appear to reach the stationary observer "at the same time", but not so for the observer on the train - the notion of "simultaneity" is in doubt.

He gives credit to Lorentz - for his work of Lorentz Transformation - and incorporates it into his Special Theory of Relativity. Relative motion is no longer a simple additive relation but a more complicated one - though still manageable.

Only then he mentions the Michelson-Morley experiment but in a way that makes it appear to be peripheral to the development of his theory. He also introduces Minkowski's (his teacher) spacetime quite late, in spite of the fact that the idea is central to Special Theory of Relativity from a physics and mathematics point of view. To put it simply, it is the Pythagorean Theorem with an additional dimension of time (albeit with a form much more complicated than the 3D theorem).

He introduces the General Theory of Relativity by highlighting that the conditions which the Special Theory is valid - i.e. constant velocities - severely restrict its descriptive power. Mathematically, Euclidean geometry does not work when a given region of space is not "equally dense," as in the case above. He introduces Gaussian Coordinates, which is the generalization of geometrical continua, with Euclidean geometry being a special case.

Special Relativity and General Relativity are different because spacetime is "equally dense" (i.e. flat) in Special Relativity, since only constant velocity cases are considered; but this is not so in General Relativity. The Gaussian coordinate system is necessary to describe them. GR can then be formulated as "All Gaussian coordinate systems are essentially equivalent for the formulation of the general laws of nature." He concluded by considering the application of GR in cosmology, with such implications as perihelion of Mercury and unbounded yet finite universe.

By this point (that is, if you had patiently read this far), you might question my addition of the precis of the book here. "Couldn't I just google it?" But chances are that introductions to Special and General Relativity are similar elsewhere, and this is how Professor Einstein did it. If you had read Walter Issacson's Einstein: His Life and Universe or Abraham Pais's Subtle Is the Lord: The Science and the Life of Albert Einstein (the latter is even more technical), this book should also demonstrate how Einstein thinks - idea first, mathematics second!

True, the theories are not something simple to grasp; but I am doing economics yet enjoy reading it - not to mention I am able to get the idea! The style of English is admittedly a little archaic but that is a relatively (no pun intended) small impediment of appreciating this great work. I would recommend that you set apart some moments in a quiet surrounding so that you could concentrate on following his arguments - that's the best way of reading the book IMHO! ... Read more

Product Description
From the Commentary by Robert Geroch (The corresponding section of Einstein’s text can be found below the comment.Please note that in the book, the Commentary is placed after the complete text of Relativity.)

Section 17.Space-Time

Minkowski’s viewpoint represents a "geometrization" of relativity. These ideas have, over the years, come to the forefront: They reflect the perspective of the majority of physicists working in relativity today. Let us expand on this viewpoint.The fundamental notion is that of an event, which we think of as a physical occurrence having negligibly small extension in both space and time. That is, an event is "small and quick," such as the explosion of a firecracker or the snapping of your fingers. Now consider the collection of all possible events in the universe—all events that have ever happened, all that are happening now, and all that will ever happen; here and elsewhere. This collection is called space-time. It is the arena in which physics takes place in relativity.The idea is to recast all statements about goings-on in the physical world into geometrical structures within this space-time. In a similar vein, you might begin the study of plane geometry by introducing the notion of a point (analogous to an event) and assembling all possible points into the plane (analogous to space-time). This plane is the arena for plane geometry, and each statement that is part of plane geometry is to be cast as geometrical structure within this plane.This space-time is a once-and-for-all picture of the entire physical world. Nothing "happens" there; things just "are." A physical particle, for example, is described in the language of space-time by giving the locus of all events that occur "right at the particle." The result is a certain curve, or path, in space-time called the world-line of the particle. Don’t think of the particle as "traversing" its world-line in the same sense that a train traverses its tracks. Rather, the world-line represents, once and for all, the entire life history of the particle, from its birth to its death. The collision of two particles, for example, would be represented geometrically by the intersection of their world-lines. The point of intersection—a point common to both curves; an event that is "right at" both particles—represents the event of their collision. In a similar way, more complicated physical goings-on—an experiment in particle physics, for example, or a football game—are incorporated into the fabric of space-time.One example of "physical goings-on" is the reference frame that Einstein uses in his discussion of special relativity. How is this incorporated into space-time? The individuals within a particular reference frame assign four numbers, labeled x, y, z, t, to each event in space-time. The first three give the spatial location of the event according to these observers, the last the time of the event.These numbers completely and uniquely characterize the event. In geometrical terms, a frame of reference gives rise to a coordinate system on space-time. In a similar vein, in plane geometry a coordinate system assigns two numbers, x and y, to each point of the plane. These numbers completely and uniquely characterize that point. The statement "the plane is two-dimensional" means nothing more and nothing less than that precisely two numbers are required to locate each point in the plane.Similarly, "space-time is four-dimensional" means nothing more and nothing less than that precisely four numbers are required to locate each event in space-time. That is all there is to it! You now understand "four-dimensional space-time" as well as any physicist.Note that the introduction of four-dimensional space-time does not say that space and time are "equivalent" or "indistinguishable." Clearly, space and time are subjectively different entities. But a rather subtle mixing of them occurs in special relativity, making it convenient to introduce this single entity, space-time.In plane geometry, we may change coordinates, i.e., relabel the points. It is the same plane described in a different way (in that a given point is now represented by different numbers), just as the land represented by a map stays the same whether you use latitude/longitude or GPS coordinates. We can now determine formulae expressing the new coordinate-values for each point of the plane in terms of the old coordinate-values. Similarly, we may change coordinates in space-time, i.e., change the reference frame therein. And, again, we can determine formulae relating the new coordinate-values for each space-time event to the old coordinate-values for that event. This, from Minkowski’s geometrical viewpoint, is the substance of the Lorentz-transformation formulae in Section 11.A significant advantage of Minkowski’s viewpoint is that it is particularly well-adapted also to the general theory of relativity. We shall return to this geometrical viewpoint in our discussion of Section 27. ... Read more

Customer Reviews (11)

Who typset the math in this thing?
I realize that this is a layman's version of the theory, but couldn't someone at the publisher really take the time to typeset the equations correctly? They don't make any sense and they aren't set up right.

Also, although this is translated from Einstein's German version, there are books that better explain his theory of Relativity. He wasn't all that good at it.However, it is an inexpensive alternative for my research.

Like Science?
I am more interested in biology-related science, but someone recommended this book. I enjoy reading these 'popular' works by great scientists and this one did not disappoint. While you need an understanding of physics to read this book, the information within explains the concepts very well. The math does get more complex towards the end and was confusing to me.

I have not read the regular edition vs. this one, so I can not comment on the differences. While some concepts were difficult to understand initially, I recommend this book for people interested in science (whether this edition or another edition).

classic
This is a classic science book. While Einstein recommended it for college students, it would be appropriate for all students who would like to know more about physics and science, and Einstein.
While it does require a great deal of work for most people to get through, it is certainly worthwhile making the effort - if only to get the flavor of what modern physics is all about. The effort is also excellent mental training for serious science students from elementary school to graduate school.
This is a book that for most people is to be read and reread and to be kept in your library. Also recommended is "The Evolution of Physics" by Infeld and Einstein.

very thin and concise, directly caught the point
describing the most advanced science 100 years ago with relatively easy language. Einstein's own idea is pretty straight forward, better than most other interpretations.

Still confusing. . .
Einsein says he wrote this small book so everyone of college calibre could
understand Relativity, with a little thought and discipline. Unfortunately,
he wrote it in 1916, in Germany (Switzerland?) where college calibre people
knew more math than most current college calibre types. So even though he thinks he's being clear and logical, unless you have the math knowledge you won't be able to follow his thinking. Besides, my understanding is that, even over 100 years after he published the theory, very few people actually understand it.
Kudos to him for trying to explicate his reasoning - but unfortunately simple and clear to Einstein is something different to the rest of us! ... Read more

Product Description
"Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful.The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."--S. Chandrasekhar

"A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."--L. P. Hughston, Times Higher Education Supplement

"Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."--James W. York, Physics Today ... Read more

Customer Reviews (22)

Can be used for self-study as a solid introduction to GR
I bought this book mainly because of its description at the MIT OpenCourseWare webpage, which is the following:

"The GR überbuch; typically the final arbiter of right and wrong in this subject. Quite mathematically sophisticated, and rather terse."

My experience with it consists of working through the first six chapters (Part I. Fundamentals) plus apendices B and C. This amounts to the material covered in most standard first courses on General Relativity. Wald's presentation is very readable, while elegant and concise. The above mentioned chapters and apendices add up to 175 pages. It took me one third of my study time during five months to work through these pages. I found this very rewarding.

About self-study and the background necessary to read this book.

I did not use this book for self-study, but as text for the GR course I was taking. It seems to me that the book is adequate for self-study, because I got a lot out of it even though the lectures differed greatly from Wald's presentation and choice of topics.

There aren't many specific prerequisites for reading this book, since General Relativity doesn't build up on (almost) anything - it is (in some sense) fundamental. Freshmen Calculus, Physics and Linear Algebra plus some Mathematical/Physical maturity are all that is needed. Maturity is the most serious requirement. I took General Relativity as a fourth year Mathematics undergraduate. I had no preparation in Special Relativity and at some point it felt like I had a logical but lacked a physical understanding of some formulas. My way around this was refering to the more conversational, introductory book on Special Relativity by Taylor and Wheeler Spacetime Physics.

One more time through General Relativity
A couple of months ago I decided to carry out some research in quantum gravity, mainly in connection with the model recently proposed by Petr Horava. A brief review of General Relativity was, then, in order. My old books on the subject, "Gravitation and Cosmology" (S. Weinberg) and "The Classical Theory of Fields" (L. D. Landau and E. M. Lifshitz), are OK but I felt I should read another book. The recommendation from my colleagues was almost unanimous: General Relativity by Robert Wald. I really like it.

Bob Wald's book
I am probably a bit biased being that Bob Wald is friend of mine and I am a former student but here it goes.

Wald's book (based on Bob Geroch's lectures) is a wonderfully concise and intuitive book for any inspiring relativist.The cosmology is certainly a bit dated and some comments are correct for the time but no longer apply with the advent of modern computing.Despite these draw backs, his treatment of linearized gravity (ala perturbation theory) as well as the Action Appendix are pure gems.He discusses the Palatini approach and shows that with the Einstein-Hilbert Action that they are one and the same.However, this little section was part of the inspiration to develop modified gravity theories in the Palatini Formalism and to show that they are different than the Einstein Formalism.I particularly enjoyed the Conformal transformation appendix and the Chapters 7 and 9 from his book.As for being an Introduction to GR, I would not recommend it for astrophysics students or classes that are hybrid graduate/undergraduate.It is for serious students of GR.Combined with John Friedman's lecture notes and De Carmo's Differential Geometry text, the student can with what passes for ease begin work in General Relativity.

A beautiful book

Something that seems to seldom be addressed in recommended textbooks for university courses is the degree to which different books suit different people. I own two other General Relativity books: MTW and Dirac's book. Additionally I have often used Weinberg's book. Wald's book again and again has been the book that I have got the most out of when seeking to understand some particular facet of the subject more.

I suppose that the book may appeal to more geometrically and mathematically minded people (the emphasis on geometry being in stark contrast to Weinberg's book). One may argue that other textbooks are superior for giving an intuition about the most familiar consequences of general relativity but I think this book is amongst the very best in terms of providing a solid mathematical toolkit with which one can use to approach an arbitrary problem. I guess this is one definition of understanding General Relativity!

excellent but beware of small books on large and complex topics
Wald is excellent, but realize what you're purchasing.Wald is a very compact book for such a large and complex topic.IMHO it is a monograph of MTW's Gravity - that is, it assumes you already know General Relativity and attempts to build upon that.

Allow me to ramble and digress.If you're coming in from the cold (ie. college sophmore level physics and math), be prepared to invest in a few other books.In my case, I bought Wald a couple of years ago.I plowed through Part I. Fundamentals and after honest reflection, realized the book was raising more questions than answers.If you find yourself going to google more than reading, that's a sign it's happenning to you!

Wald may seem like a bargain (<$50) but here's the cash outlay from supplemental books:
1. Hartle, Gravity, ~$50.Provides problem solving mechanics of applying einstein's equation.
2. Carroll, Spacetime and Geometry, ~$50.Provides a few derivations which Hartle leaves out.
3. MTW, Gravitation, ~$125.Provides intuition and visualization to Einstein's equation.
4. Schutz, A First Course, ~$30.This book is optional.I only read this because alot of other people did.It's essentially an attempt to dumb down general relativity at the undergraduate college level.

So why do I rank this text 5 stars.After reading the texts above Wald's purpose became immediately clear - to modernize MTW from a mathematical perspective.Wald succeeds with flying colors.For example, I was especially excited discovering and realizing after re-reading Wald that the proof of theorem 2.2 was a detailed answer to one of my homework problems in my differential topology class! ... Read more

Product Description
"This beautiful little book is certainly suitable for anyone who has had an introductory course in physics and even for some who have not."--Joshua N. Goldberg, Physics Today

"An imaginative and convincing new presentation of Einstein's theory of general relativity. . . . The treatment is masterful, continual emphasis being placed on careful discussion and motivation, with the aim of showing how physicists think and develop their ideas."--Choice ... Read more

Customer Reviews (7)

interesting nonmathematical take; sometimes poor motivation and contact with experiment
This is a quirky book with an interesting idiosyncratic take on general relativity. It has a good, intelligible story-line that starts with the Aristotelian view of space and time, then moves on to Galileo and then to Einstein.

The heart of the book is the following construction. Suppose we have two events in spacetime, p and q. Define something called the "interval" between p and q by the following measurement procedure. (What I'll give is just one of the five cases he describes, the one in which no light ray can get from p to q or from q to p.) Let observer O, who has a clock, emit a photon that can be received at q. Let O then visit p, recording the elapsed time t2. O then resets his clock to zero. Meanwhile, the photon received at q is re-emitted back toward O. Finally, after an additional time t1, O receives the second photon. Define the interval as the product t2t1.

The definition of the interval is cute because it's extremely spartan. It requires almost no preliminary mathematical apparatus such as coordinate systems. On the other hand, I felt that Geroch didn't properly motivate the definition. He just pulls it out of his hat, says that nobody can ever know why this particular definition is appropriate for our universe, and only much later provides any reasoning that would allow the reader to see why it should be that way. He also has to introduce some approximations which are kind of ugly and not very clear (about p and q being sufficiently nearby). There's a lot of ugly case-splitting (five different cases, depending on whether p is in q's timelike lightcone, etc.).

The contact with experiment is very weak. You can tell that Geroch is a theorist.

astonishing
For the last month, this book has been a great lunch-time companion.My favorite aspect of this book is not the fact that it explains relativity at a very deep level, but that it explains, at a very deep level, how a scientist thinks.I recommend this book to anyone who enjoys concentrated thinking (this book demands it!) I'm going to try to get my own son to read it.

Excellent Book
This really is a great book on general relativity. While it is not mathematically intensive, it is not just a simple introduction as one of the reviews here stated. While it's not a college course on the subject, I believe this book would enlighten many who have studied general relativity and give them some insights they didn't have before. Physics, after all, does translate to real concepts in the physical world. I never accepted the notion that certain things could only be known if you have a mathematical background (which I do have.) Ultimately, the math must mean something in the physical world and it's just a matter of teaching it properly, using the right metaphors, etc. This book does that very very well. I've read it a few times and will read it again in the future. There are certainly other aspects of general relativity that you can expand on, and there it certainly gets much more involved and complicated than what's presented here, but this is really a gem.

Verbal Description of General Relativity
The author presents fundamental ideas of theory of relativity in a non-mathematical form using conversation approach to readers with little science background. The book is highly descriptive and the reader is bound to get bored since this is a discussion of about basic ideas about space and time using two-dimensional space-time diagrams. The first part of the book describes the notion of space and time in terms of Aristotelian and Galilean view points. The second half describes how the idea of spatial distance and elapsed time (interval) are incorporated into space time as geometrical entity. The author uses a general framework in this book for explaining general relativity. This is done by describing an event and assemble them into space-time (in a space-time diagram) and describe what is going-on in the physical world in terms of collection of events, and relationships between events is evaluated using measuring instruments such as light pulses and clocks. The intrinsic relationship between two events is described by interval (measured by physical experiences of observers). From the interval, one determines how light goes and how clock move and tick. The author eventually explains how equating intervals leads to relationship between `real' physical measurements. The interval is a sort of misty thing that stands in the background and integrates into space-time. In the final chapter the author discusses an application of general relativity to understand the properties of blackholes: It is here that the readers appreciate the importance relativity.The reader must have patience to read this book and he/she must be prepared to read chapters 5 and 6 second and perhaps third time to understand the underlying concept. If you do not have patience you will be lost and you will dislike this book

A Grand First Step.Well, maybe a quarter step..
This still ranks as one of my favorite relativity books.There is virtually no math to speak of.Yet, the author in a very descriptive way, will take you from Aristotelian view to the Galilean view and finally to the relativistic paradigm.Concepts such as events, event horizons, interval etc. are explained quite beautifully.The idea of the interval and the physics and geometry of the same is shown in a most interesting way.

The chapters are organized very well and the writing is very good.To follow the text a certain degree of concentration is required because the diagrams need to be checked as one proceeds.

This text is quite suitable for junior high and high school students not to mention college graduates who wish to know something beyond the cursory in relativity theory.

I happened to come across this book at a used bookstore in 1979.Very few of my friends were even aware of this book.It was one of those sleepers so much so that a while back this volume had gone out of publication.However, now it's back, thank God. If you want a non-technical but quite thorough peek into Special Relativity get this book.If you are one of those who would prefer a tad more math and a less wordy introduction go with James A. Smith'sAn Introduction To Special Relativity, published by Dover. ... Read more

Product Description
After reviewing the basic concept of general relativity, this introduction discusses its mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle. ... Read more

Customer Reviews (3)

big problems
I was the TA for an undergraduate course that used this book.I read the book to reference equations when writing up homework solutions, and in response to students questions about it, but not otherwise.That is, I did not read it cover to cover, but selectively.However, almost invariably when I read a section I would think that something in it was either confusingly presented or simply wrong.I kept a list of my "grievances" as the semester went along, and I am writing them as part of this review.I probably should give the book one star, based on my experience, but since I haven't read very much of it, it's conceivable that other parts are very good.(So, it gets two stars.)Also note that the students uniformly complained about the book.

1.P. 10, treatment of length contraction.The equation for length contraction is "derived" with no discussion of simultaneity.Essentially, the book writes dx = gamma ( dx - v dt ), and sets dt=0 so that dx is "length".This is not a correct derivation without more explanation, because (for example) using the inverse Lorentz transformation would give the opposite answer.None of the words in the book explain why the the Lorentz rather than inverse Lorentz transformation should be used.It's just not possible to give a correct treatment of Lorentz contraction without being careful about the notion of simulteneity.(It also would help to have a spacetime diagram.)You need to say what length means in each frame, and then compare them.This came up because I was giving students very little credit on a homework problem that was essentially "derive length contraction", and it turned out they had copied out of the book.

2.P18,p117, notation for three-velocity.The book adopts the totally absurd convention of denoting the three velocity by \vec{u} and the four-velocity by u^alpha.Of course, the three-velocity is not equal to the spatial components of the four-velocity, so this notation is incredibly confusing (if not inconsistent, since u^1 would denote both the 1 component of u^alpha and of \vec{u}).A veteran of relativity can follow even an inconsistent notation, but this is incredibly confusing for somebody trying to learn the subject (which is the point of the book).I got lots of confused questions from students about this one, and no surprise.There are plenty of letters in the alphabet--choose a different one for the three-velocity!

3.p120, second paragraph.This one is so ridiculous I can't believe it made it past the first reprinting.The authors write, "So far, we have not mentioned the frequency (or energy) of the photon, which characterises it in much the same way as the rest mass m_0 characterises a massive particle."This is of course completely false.The rest mass is an invariant quantity, whereas the frequency/energy depends on the frame.The analog of the rest mass for photons is zero, the invariant quantity of zero rest mass.The analog of photon energy is particle energy.Frequency has to do with quantum mechanics and has no analog I'm aware of.This sentence sticks out like a sore thumb to anybody who has done some special relativistic kinematics.Again, I simply can't believe it wasn't caught as a mistake by the reprinting.

4. p21, discussion of uniform acceleration.This is a more minor point, but I don't think the authors do a good job of explaining the concept of "uniform acceleration".Uniform acceleration usually does me "uniform four-force", which is very confusing terminology.I think the authors could do a better job of pointing this out.Let me emphasize that this point is minor in comparison with the others

5. p123.The authors say that free particles move on "non-null" worldlines, rather than on "timelike worldlines".Again, this sticks out like a sore thumb; it should have been caught and fixed.

6. p183 and elsewhere.The authors write R^{\mu}_{\nu} instead of R^{\mu}_{\ \nu}.While it is indeed unambiguous to do this for symmetric tensors, I don't see the point.There is a perfectly good notation that works for all tensors, and doesn't need statements like "by the way you can check that both natural interpretations of this notation are in fact equivalent" to define it.Why confuse students with an index operation that is only okay for certain tensors?They are trying the best to get to grips with index notation, already.I think this is a very poor decision pedagogically.

7.p188-189, treatment of point particles.The authors give a very silly discussion of point particles in general relativity.To be clear, there are no solutions in general relativity with point particle stress-energy (see the paper by geroch and traschen).Yet, the authors say (for example) "the position of the particle is where the field equations become singular".It is fine to present the calculation that point particle stress-energy will be conserved only for geodesic motion, but don't pretend there is anything more to it than a (very) suggestive calculation.Since no solutions exist for that stress-energy, you haven't shown anything about the motion of particles in GR.(At the very least, don't discuss the field equations without pointing out that there are no solutions!)

Again, I haven't read the whole book, but you can understand from above why my impression of it is poor.

Great Book
I have this book along with the classic by Misner, Thorne, and Wheeler.Both are good, but I like the explanations in this book better.I think it benefits from being published in 2006.Physicists have learned how to explain General Relativity better.Misner, Thorne, and Wheeler is 3 times thicker and covers more topics, but this is actually a distraction from learning the subject for the first time.

Another advantage of being published in 2006 is that the quality of presentation has improved.

I recommend the book.

An excellent Introduction
While looking for a book to teach my undergraduates I was lucky to obtain a copy of thisbook.I was ready to implementthe Nightingale/Foster , but I was disappointed to seethe degradation of its second edition. I learned GR with the first edition of N/F!!!.
Well , I checked this excellent book and I was amazed.
In the first chapters the authorsexposeVectors tensors and manifold in the easierpossible way. Then they revise Special Relativity . Then , they proceed as usual , Curved spaces , Einstein's Field Equation , Scwh-Metric, Schw -Black Holes , Interior solutions, but , then : Kerr solution in great detail!!. Without going into Ehler's equations or Degenerated Algebras ,the authorsdescribevery wellKerr'sGeometry and Physics ( Penrose's , Celestial Mechanics..etc).
Cosmology ( FLW) solutions ,..Inflation in some extent!!..Linearization and Gravitational Waves (Production and detection).At the very endthere is the Hilbertactionetc.

I wish some Kaluza/Klein , which is possibleand necessary forthe new generation ( to understandcompletelyString Theoryyou need totaste KK- theory ) and also , I wisha given amount of solutionfor thelarge number of problems at the end of every chapter.

I hope to seeboth of these in futureversions of this magnificent introductory book and then I will give the 5-star. ... Read more

Product Description
A student-friendly style, over 100 illustrations, and numerous exercises are brought together in this textbook for advanced undergraduate and beginning graduate students in physics and mathematics. Lewis Ryder develops the theory of general relativity in detail. Covering the core topics of black holes, gravitational radiation, and cosmology, he provides an overview of general relativity and its modern ramifications. The book contains chapters on gravitational radiation, cosmology, and connections between general relativity and the fundamental physics of the microworld. It explains the geometry of curved spaces and contains key solutions of Einstein's equations - the Schwarzschild and Kerr solutions. Mathematical calculations are worked out in detail, so students can develop an intuitive understanding of the subject, as well as learn how to perform calculations. The book also includes topics concerned with the relation between general relativity and other areas of fundamental physics. Password protected solutions for instructors are available at www.cambridge.org/9780521845632. ... Read more

Product Description
Spacetime and Geometry: An Introduction to General Relativity provides a lucid and thoroughly modern introduction to general relativity. With an accessible and lively writing style, it introduces modern techniques to what can often be a formal and intimidating subject.Readers are led from the physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology.For advanced undergraduates and graduate students, or anyone interested in astronomy, cosmology, physics, or general relativity. ... Read more

Customer Reviews (12)

Great GR book to learn GR from
I'm using this book as a supplement to Wald to teach myself and a few friends in my department GR. Apparently (according to my professor who was with Carroll at Harvard), thats how the book came into existance in the first place. As far as I can tell, the book is excellent. I highly recommend it. Basically it's Wald in English. Many things in Wald are explained in more detail (don't confuse detail with clarity, Wald posesses the supreme clarity of Math). Therefore, this text is best used in conjunction with Wald.

Wordy and Wonderful
This is an advanced text, but all the same it is not particularly rigorous or dense, so it is in principle accessible to the beginner.With an easy authority, Carroll leads us on a wandering journey through the mystical lands of general relativity.This is very different from, and compliments nicely, the clarity and directness of Wald.As a student of GR, I use Wald for the bottom line on any subject, and Carroll for the random physical or computational insights that I invariably find in any section of the book.Carroll's prose is like music to the ear and I always enjoy myself when I decide to open up this book.

Be warned that there are lots of mistakes in this first edition--you might want to wait for the second one.

Also, his chapter on cosmology is better than any I've seen.

BY FAR the best book on GR
I am currently on the 4th chapter of Carroll's "Spacetime and Geometry" and thus far I am amazed at how clear it is.Sure there is a lot of math in it however that also is very clearly explained.In fact, I think that Carroll explains the differential geometry material better than any mathematician has in any book on the subject.If you want to learn general relativity, there is no getting around the math; sooner or later you'll have to learn it.I'd suggest, especially if you are self-studying the subject, to rather pick up this book and go through it than pick up a more "elementary" text and a book on Riemannian geometry to look at later.

(Although I do also highly recommend Kay's (Schaum outline) "Tensor Calculus" for self study.The prima donnas don't like Kay's book because it "doesn't have enough theory."I suppose if a freshman calculus book does not have the Lebesgue integral defined in ti they'll complain about that too.)

Because, you can always skip through certain sections if the math is too heavy and go back through it later.And like I wrote earlier, you won't find a better introduction to the mathematical material than here.

Carroll should be given the Nobel prize for this book.If not in Physics, then in literature.I'd give this textbook 10 stars if I could.

A nice blend of the ideas of physics with mathematics
Kudos to Carroll.

This book is an excellent INTRODUCTION to SR and GR for the graduate physics student as well as the graduate mathematics students.

Pure mathematics often loses sight of the ideas which motivated it and physics often loses the mathematical foundations from which it is built.

This book offers some level of mathematical formalism to the physics student while exposing the ideas motivating the mathematical concepts.

I particularly like how he builds up the mathematical machinery of GR by introducing sets then topology on this set giving a topological space. Now he adds in the ideas of a manifold which make this topological space look like Rn locally with the patches sewn together smoothly. The manifold comes equipped with tangent space, cotangent spaces and their product spaces giving tensor spaces. These are defined nicely with reference to component formalism as well as the multilinear algebra approach as maps from products spaces to the reals, etc. He delves into forms and tantalized the reader with deRham cohomology although doesnt go into it. He shows how these can be differentiated ( exterior derivative ) and integrated.

Now the metric is introduced giving a geometry. To this is added a connection which is independent of the metric and leads to notions of parallel transport and differentiation of tensors ( covariant derivative ). One sees that in a special case one can derive a unique connection from the metric ( Levi-Cevita ) which is used in GR.

Fibre bundles, Lie derivatives, pullbacks etc are introduced as needed.

He then presents some introductory GR material by applying the mathematics.

Great Book But Won't Get You To The Promised Land
My comments come with a few caveats.

1. This is my fourth GR book.
2. I'm not hardcore into physics.I'm not a physic grad and I'm reading GR for fun.I have a decent graduate math background but I've been corrupted with 10+ years in working in various roles software engineering, electronics engineering and marketing.
3. I assume that since you're considering buying this book, you're goal is to get at the "real" GR, not the watered down discover channel version.

With these caveats in mind, here are my comments.

First, on a scale of 1-5, I rank Carroll at level 3 in terms of math/physics maturity and thoroughness.Here is my full ranking of authors from my limited reading:1. schutz2. hartle3. penrose3. carroll 4. wald5. physics journal articles

Second, using the rankings above, I recommend Carroll as the second port of entry.If you're comfortable with multivariable calculus, start with schutz (#1). You'll get warm fuzzies doing the toy exercises. But Schutz is tensor/math-lite.If you've had advanced calculus and geometry already, jump in with carroll (#3).But you'll be hard-pressed to find anyone else as polite to the reader.He won't prepare you for 80 percent of what's published.If you're ready to throw off the training wheels and jump dive into mainstream GR go with Wald (#4).

Note that Hartle (#2) is a good "tweener" book with feel-good exercises and some of the full-on GR equations at the end.I bet most instructors teaching a first year grad course would go with Hartle along with a dose of supplementary material.

Third, don't expect Carroll to be your last GR book purchase if you want to reach the promised land (see caveat #4).Living and breathing GR is found in physics journals and for that you'll need Wald or another advanced GR book. ... Read more

Product Description
A working knowledge of Einstein's theory of general relativity is an essential tool for every physicist today. This self-contained book is an introductory text on the subject aimed at first-year graduate students, or advanced undergraduates, in physics that assumes only a basic understanding of classical Lagrangian mechanics. The mechanics problem of a point mass constrained to move without friction on a two-dimensional surface of arbitrary shape serves as a paradigm for the development of the mathematics and physics of general relativity. After reviewing special relativity, the basic principles of general relativity are presented, and the most important applications are discussed. The final special topics section guides the reader through a few important areas of current research.This book will allow the reader to approach the more advanced texts and monographs, as well as the continual influx of fascinating new experimental results, with a deeper understanding and sense of appreciation. ... Read more

Customer Reviews (1)

A good first book on general relativity

In 1905, with the Special Relativity (SR) theory, Einstein brought a completely new idea into the field of physics: space and time are not two separate entities (or "categories", as Kant had named them two centuries before), but they are related in some special way.By changing (inertial) reference system, i.e. by traveling with a different velocity, one can "transform" a bit of time in space and vice versa.This revolutionary idea left open the question about the _nature_ of inertial systems.Einstein was wondering what happens if, instead of changing my velocity with respect to the far stars, I move the entire universe in the opposite direction.The SR is completely symmetrical: two inertial observers will note the same effects when looking at the phenomena happening in the other's reference system.

On the other hand, the SR makes a neat distinction between uniform motion and accelerated motion, something which is also very near our common sense.For example, if we rotate a container filled with some water (and the water is also dragged to rotation), the surface of the water will change from a flat surface at rest to a concave shape due to the inertial force known as centrifugal force.On the contrary, if we leave the container still and _we_ sit into a reference frame which is rotating around the container, we do _not_ see a change on the shape of the water surface, but we (not the water) _feel_ the centrifugal force.However, what would happen if the entire universe were rotating around the container?We feel that, when speaking about "the entire universe", we should point to some very special reference system: we feel that the shape of the water surface _should_ change in this case.But there is no space for this kind of effect in SR: there is no preferred or special reference system in this theory.

The General Relativity (GR), when first introduced by Einstein, about a dozen years later than SR, represented a very new step in the history of science.The GR is a theory of _inertia_: it says (in axiomatic form) that the reference frame "attached to" a freely falling observer is _locally_ an intertial system.A freely falling observer is simply somebody (or something) who is moving without propulsion in a gravitational field.Because the observer is in a (local) inertial system, she can make use of the SR to describe all physical phenomena.

For example, a satellite orbiting around the Earth is a freely falling system, as long as its dimensions are small compared to the typical scale on which one is able to measure different values for the Newton's gravity force.The astronauts do not feel any gravity at all, and they can perform (small) experiments to verify that they really sit in an inertial reference system.To a quite good precision, the planets in the solar system are freely falling, even though the tides remind us that the Earth is not as small as a good inertial system would ideally require.In addition, the solar system itself can be considered an "object" which is freely falling in the gravitational field of the Galaxy, and so on.As long as one can neglect "tide" effects, everything is freely falling in the universe!

But the GR says more than this: inertial observers follow the _geodesics_ of the spacetime.Because the source of gravity is the energy (in _any_ form, like mass or momentum), the distribution of energy defines the geometry of the spacetime.In other words, a small test mass which is left free to move (i.e. has no propulsor) will follow a trajectory in the spacetime which is defined by its initial conditions (position and velocity) and by the distribution of the masses all around---of the whole universe, in principle.Hence, the inertial motion depends on the universe configuration: if we could rotate the whole universe, we should see a change in the shape of the water surface!In the GR, we can find a sort of "special" reference systems, and this is experimentally confirmed: the angular distribution of the cosmic microwave background (CMB) radiation (the relic radiation from the hot Big Bang) has a dipole shape which is providing us a way to measure the _absolute_ (i.e. with respect to the special reference system) motion of the solar system.Once we correct for this dipole effect (i.e. we move to a reference system at rest, with respect to the special one), the distribution of the CMB is extremely flat, the fluctuations being at the level of a hundredth of percent.

This is how the GR is usually introduced: first one emphasizes the two basic ideas that a freely falling system is a local inertial system and that it follows the geodesics of spacetime, defined by the distribution of energy in the universe; then one develops the (complicate) mathematical tools needed to address problems in this new framework.However, the time has come to provide the students with a smooth transition from the classical mechanics to the GR, as in the book by Walecka.This already happened with all earlier "revolutions" in the history of science (still it has to happen with quantum mechanics): today, nobody is marveled how the Maxwell's equations are introduced by physics textbooks, just to make one example.Walecka introduces the differential geometry when addressing classical problems, and shows that the Newton's equation can be reduced to a motion along a geodesics also in classical problems.Simply take a system with some mechanical constraint and choose a set of generalized coordinates which reflects the actual degrees of freedom of the system: the Euler-Lagrange equations in these coordinates are the equations of the geodesics in themetric defined by the coordinate transformation.This way, the student is taught the mathematical tools without being "distracted" with the new, powerful, ideas of GR.

Once that things like tensor analysis, the affine connection, covariant derivatives, Riemann's and Ricci's tensors are introduced, Walecka starts speaking about SR and GR.In the first seven chapter, all the theory is exposed.The rest of the book is about applications of GR to solve problems like the orbital motion of the planes, the deflection of light, the gravitational and cosmic red-shifts, the neutron stars, the evolution of the universe, and the gravitational waves.Here, I should say that not all these items are addressed with the same depth, expecially the very last topics.However, a good literature exists on all of them and the book by Walecka provides the student with all the background one needs to browse the more advanced treatments.

In conclusion, this book is probably one of the best choices as a first book on general relativity, because it guides the student through the path of minimum steepness toward the goal of understanding and learning this fascinating theory.I did not assign the maximum rate to it only because it is not very complete when addressing the very last topics.However, a fuller treatment of those would have required almost twice the number of pages of the present volume!
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Product Description
Einstein's general theory of relativity requires a curved space for the description of the physical world. If one wishes to go beyond superficial discussions of the physical relations involved, one needs to set up precise equations for handling curved space. The well-established mathematical technique that accomplishes this is clearly described in this classic book by Nobel Laureate P.A.M. Dirac. Based on a series of lectures given by Dirac at Florida State University, and intended for the advanced undergraduate, General Theory of Relativity comprises thirty-five compact chapters that take the reader point-by-point through the necessary steps for understanding general relativity. ... Read more

Customer Reviews (18)

GR in 2 pages per Chapter
Yes, that's exactly the way i've entitled it. So, it should be used just as a quick reference guide to find some equation(s) you need when you already have studied and understood them. I mean, don't expect to understand GR from this small (nice)book. It is like a sumary of the whole theory as it was standing at the time Dirac wrote it. Therefore it does not contain solutions to Einstein equation but the Schwarzschild one. No Kerr-solution, no Finkelstein coordinates, no causal structure...

But anyway, maybe we could say it is the most fast/first-level source you can take a look to find clear equations and clear 1-paragraph-explanations.
For the price you can have it, I think it is a good purchase once you have passed through really teaching books like i.e.: Schutz, Weinberg, Wald, Hawking-Ellis...(in order of increasing mathematical hardness).
Math notation friendly.
No exercices.
Just what i said, 2 pages per chapter.

one of the most important surveys on general relativity already published
Paul Dirac was one of the most celebrated physicists in the history of physics. His "General Theory of Relativity" is a survey on the topic, but what a survey...

A pleasant way to review differential geometry
I've no interest in general relativity, but I have twice enjoyed reading the first part of the book because it is a succinct, elegant review of differential geometry. Light of mass and heavy of meaning, it makes a great companion on a long airplane flight.

You hear him speak
I took the course the book is based on in the Spring of 1973. We students took turns taking notes until the last few where for some reason we ran out of volunteers. The book is an excellent condensing of the lectures. Many of the steps are left out that were presented in the lectures or left for the students to fill in. While there are no explicit exercises in the book, going from one step to the next provides an excellent opportunity to test your understanding. I am in no way an expert in mathematics, but the equations are sufficient to follow point to point.
When I read this book, I can hear him speaking. He would have the day's lecture on a 3x5 card that he would look at at the start and perhaps one more time during the lecture. He had the ability to lecture on GR or quantum mechanics and you would sit there and say "Yes, that makes sense. Now I understand." They you would walk out and start thinking and come to the conclusion that you really didn't understand and that you needed to study it some more. This book lets you do that.

Crash course in Diff. Geometry aspects of General Relativity
This book is a marvel of presentation and concision.
However, you should not regard it as a first course on the subject, unless you merely want to learn its formal aspects.
As such, the subject would appear as a mere pot-pourri of formulas and mathematical concepts directly borrowed from a differential geometry course, with just a little grain of physics ideas.
Almost no mention is made of general relativity experimental tests or the ideas that led Einstein to formulate this theory ; nothing deep and elaborate on stars, the expanding universe ; there's not much on black holes beyond the section about the Schwarzshild coordinate singularity.
To really grasp the subject, you will have to be committed to much more hard and patient work from thicker books.
Reading this book, would be excellent for motivational purposes.
With such warnings in mind, go for it. ... Read more

Product Description
Aimed at advanced undergraduates with background knowledge of classical mechanics and electricity and magnetism, this textbook presents both the particle dynamics relevant to general relativity, and the field dynamics necessary to understand the theory. Focusing on action extremization, the book develops the structure and predictions of general relativity by analogy with familiar physical systems. Topics ranging from classical field theory to minimal surfaces and relativistic strings are covered in a homogeneous manner. Nearly 150 exercises and numerous examples throughout the textbook enable students to test their understanding of the material covered. A tensor manipulation package to help students overcome the computational challenge associated with general relativity is available on a site hosted by the author. A link to this and to a solutions manual can be found at www.cambridge.org/9780521762458. ... Read more

Product Description

The foundations are thoroughly developed together with the required mathematical background from differential geometry developed in Part III.

The author also discusses the tests of general relativity in detail, including binary pulsars, with much space is devoted to the study of compact objects, especially to neutron stars and to the basic laws of black-hole physics.

This well-structured text and reference enables readers to easily navigate through the various sections as best matches their backgrounds and perspectives, whether mathematical, physical or astronomical.

Very applications oriented, the text includes very recent results, such as the supermassive black-hole in our galaxy and first double pulsar system

Customer Reviews (1)

A Masterpiece
For the graduate student of physics or mathematics who has the requisite background in modern differential geometry, Straumann's text presents themost mathematically honest and thorough introduction to general relativity currently available in book form.This book is a masterpiece and belongs in the company of the classic books by Misner, Thorne and Wheeler, Penrose and Rindler, and Hawking and Ellis.

Potential readers must understand that there has been an uneasy truce between modern differential geometry and general relativity for nearly a century.While mathematicians developed the subject of Riemannian geometry along largely coordinate-free lines, reaching ever greater levels of abstraction and geometric insight, physicists continued to develop the related subject of semi-Riemannian (also called pseudo-Riemannian) geometry along coordinate-based lines, mired in complex index computations and the awkward notation that accompanies them.This is reflected in the Introduction to an excellent 1990 text on semi-Riemannian geometry in which the authors, explaining their choice of title, offer the semi-humorous lament, "Any possible title would mislead somebody.'Tensor Analysis' suggests to a mathematician an ungeometric, manipulative debauce of indices, with tensors ill-defined as 'quantities that transform according to' unspeakable formule."

Misner, Thorne and Wheeler introduced a generation of students to the power of modern, coordinate-free methods in general relativity in the early 1970s in their classic book "Gravitation," citing the wonderful book by Bishop and Goldberg as their standard reference forsemi-Riemannian geometry.Sadly, however, the modernization of the subject that MTW initiated did not seem to entirely catch on within the physics community.A number of very recent texts on general relativity have been printed in the past decade by highly reputable publishers, all written in an entirely index-based approach that was already becoming outdated and deficient over 30 years ago.The serious student of relativity already faces considerable challenges in mastering the formidable mathematical preliminaries to the subject;the work surely need not be compounded in difficulty by total reliance on obscure, unmotivated, index-based computational gymnastics. What students need is a thoroughly modern and enlightened introduction that teaches them to move comfortably and effortlessly between index-free and index-based approaches, permitting them to read and understand both the older and modern literature, both the physics and mathematical literature.

Straumann's book offers an introduction to general relativity that is completely modern in its approach to the mathematics.The final five chapters, covering roughly 100 pages, provide concise but readable introductions to basic manifold theory, Lie differentiation, differential forms and integration on manifolds, and the theory of affine connections (this latter does not provide an introduction as thorough as is found in volume 1 of Kobayashi and Nomizu---there simply is not room to study Ehresmann's approach to connections in this overview).Any student who has been fortunate enough to study the mathematical preliminaries from a modern treatment, such as Barrett O'Neill's wonderful Semi-Riemannian Geometry with Applications to Relativity, will be able to master the mathematical material in Straumann without undue stress.

One final piece of history to fully drive home the point. Richard Bishop and Barrett O'Neill introduced the notion of warped product manifolds to Riemannian geometry in the 1960s, providing one way of decomposing amanifold into two smaller and "simpler" parts.Beem and Ehrlich observed in 1982 that many of the well-known exact solutions to Einstein's equations are natural examples of warped products.The use of warped product formulas offers significant simplification of the analysis of these exact solutions.The use of warped products became central in O'Neill's 1983 book on semi-Riemannian geometry, and in Beem, Ehrlich and Easley's 1996 book on Global Lorentzian Geometry.Other authors have been slower to recognize and employ this powerful tool, and the reader will barely find warped products mentioned at all in modern texts on general relatitivy. In stark contrast, Straumann's book contains an entire section on warped products and makes full use of the simplifying formulas throughout:another sign of the progressive nature of the book.

I recommend this book in the strongest possible terms to all serious students of general relativity.If your background in differential geometry in inadequate, then I recommend purchasing O'Neill's book along with Straumann's as a packaged set.I view the O'Neill/Straumann pair as the current successors to the tradition begun by the Bishop and Goldberg/Misner, Thorne, and Wheeler books of an earlier era.

Dr. Straumann already updated this book in 2004 to a far more extensive second edition.We can only hope that as developments in our understanding of the large-scale structure of the universe progress through observational astronomy, Dr. Straumann will continue to update his book to include recent experimental and theoretical results.




... Read more

Product Description
A graduate level text on a subject which brings together several areas of mathematics and physics: partial differential equations, differential geometry and general relativity. It explains the basics of the theory of partial differential equations in a form accessible to physicists and the basics of general relativity in a form accessible to mathematicians. In recent years the theory of partial differential equations has come to play an ever more important role in research on general relativity. This is partly due to the growth of the field of numerical relativity, stimulated in turn by work on gravitational wave detection, but also due to an increased interest in general relativity among pure mathematicians working in the areas of partial differential equations and Riemannian geometry, who have realized the exceptional richness of the interactions between geometry and analysis which arise. This book provides the background for those wishing to learn about these topics. It treats key themes in general relativity including matter models and symmetry classes and gives an introduction to relevant aspects of the most important classes of partial differential equations, including ordinary differential equations, and material on functional analysis. These elements are brought together to discuss a variety of important examples in the field of mathematical relativity, including asymptotically flat spacetimes, which are used to describe isolated systems, and spatially compact spacetimes, which are of importance in cosmology. ... Read more

Product Description
Relativistic cosmology has in recent years become one of the most exciting and active branches of current research. In conference after conference the view is expressed that cosmology today is where particle physics was forty years ago, with major discoveries just waiting to happen. Also gravitational wave detectors, presently under construction or in the testing phase, promise to open up an entirely novel field of physics.

It is to take into account such recent developments, as well as to improve the basic text, that this second edition has been undertaken. The most affected is the last part on cosmology, but there are smaller additions, corrections, and additional exercises throughout.

The books basic purpose is to make relativity come alive conceptually. Hence the emphasis on the foundations and the logical subtleties rather than on the mathematics or the detailed experiments per se. Aided by some 300 exercises, the book promotes a deep understanding and the confidence to tackle any fundamental relativistic problem. ... Read more

Customer Reviews (6)

Unavoidable
This book is an update of the author's previous work "Essential Relativity," although the former book remains available through another publisher."Essential Relativity" contains interesting (to me) material that had to be omitted from the new volume.The new volume contains necessary updates.The author is a world class scholar, and he gives a very comprehensive introduction to relativity, both special and general.Consequently, every serious student will be forced to purchase this book and study it thoroughly and quite carefully.

As churlish as it may sound, I expect more from a world class scholar, teamed with one of the top technical publishers in the world.Rindler really begins the technical discussion in section 2.7, which is a modest edit of a section from his previous book "Introduction to Special Relativity." In it, he considers a free particle whose trajectory is parameterized by its own particular clock, mu.He then considers the coordinates of two separate inertial references frames.By differentiating by mu, he is able to show that the coordinates of inertial systems have to be linearly related.A page or two later, he has derived the whole Lorentz transformation in quite a lot of detail (not perfect detail).On finding the "truth," we then see that different observers see time sources quite differently.This is not obviously consistent with the original differentiation.For beginning classes, at least, this is at least an unnecessary source of potential confusion.Compare and contrast this ponderous progression with the smooth and economical set up for the Lorentz Transformation that is to be found in the first chapter of Landau and Lifschitz's "Classical Theory of FIelds."It seems, at first, that Landau Lifschitz is at least infinitely better---maybe more.Is Rindler somehow silly, or a person of poor taste?No, that's not at all the case.He makes this choice for a clear pedagogical reason.He wants to show that the principle that physics is the same in all inertial systems is of primary importance and that the invariance of light speed in all inertial frames gives us much less information. Is that true?It could be true (read Landau Lifschitz), but it is, whatever else, the view of an important scholar, and one that every student needs to take seriously---even if it is phrased in quite a laborious and perhaps somewhat self-inconsistent way.

Rindler clearly tries to give the best possible understanding of the physics, apart from the mathematics.In that he certainly gets a partial success, but he seems to me not to get a full success.For that, I could cite his explanation of the relativity of simultaneity, time dilation, and space contraction in section 2.4.On the one hand, it is clearly independent of mathematics.On the other hand, I find it labored and unclear---perhaps poorly edited.These are very early examples in the book.To me, the whole book is something like that.It attempts to put full emphasis on the physical view while including only enough mathematics to make everything correct and essentially complete.

It is my own idea that most people will be better served to use the two volumes of N.M.J. Woodhouse (of Oxford University) on special and general relativity as a better, easier, clearer introduction.Woodhouse makes no attempt to sidestep the mathematics, and that is appropriate.There is no actual understanding of relativity apart from the mathematics.So, it makes sense to grin and embrace it.I think his is the clearer and better place to start.For special relativity, the easy book of Taylor and Wheeler is probably better (although maybe a little cheesy).Everyone will need to read Rindler at some stage.Personally, I think it better to leave it as a "have to read"---like it or not.It's aggravatingly unclear in important points.These ought to be something of an obstacle to first learning, although they will not really encumber a sophisticated reader. First become sophisticated with Woodhouse and then you can read Rindler through much more economically and without being bothered on belabored points.

Rindler is actually a world class scholar---a great man.That is not tongue in cheek or some sort of backhanded attempt to insult him.He actually is a great scholar, and I respect that.I expect great scholars to offer better writing than this.

Great Delivery Speed
The book was in perfect condition and got to my place within a couple of days after ordering it.Great speed!

no explanation of tensors, co-variance, etc.
The author does a pretty good job of explaining physical concepts, but is obviously impatient at explaining mathematics.In the chapter on electromagnetism he introduces tensor notation and important theorems such as co- and contra-variance without explanation.In some cases he says "the proof is left to the reader."The treatment is much less detailed than Einstein's original 1915 paper.It is like a book that purports to teach you French, and which summarily presents an abstract French-English dictionary and then the rest of the book is written in French.

One of the worst text on GR
This is one of the worst text I came across. Author keep discussing a topic but never points to the result. A book where you keep flipping back and forth to make sense. Often notations are used but there is no explanation what they represents. I have gone through chapter 15 and 18 ,on Linearized GR and FRW metric, following every step and found out that there are few errors and a lot of key steps are omitted. For example, gauge transformations are done and results are obtained but if you won't consult other similar texts then you won't know what are the results and which are the transformations, unless you already are a professor. Almost same topic is discussed in Inverno's book and you can clearly see what are the various transformations and what are the results.

A book may contain every topic what you are looking for but the key Qs is how well are they conveyed. In order to write an excellent text the author should be first clear about it in his own mind and organize it before publishing it. Save yourself and get a nicer book like Inverno or Stephani. I would not recommend this text for GR unless absolutely necessary.

Whoosh
Professor Rindler explains the concepts with clarity and rigour while minimising the complexities of the notation and formulae.His ability to put ideas into words is outstanding.If you have heard the tales of trains that whoosh past in the ether, and are still none the wiser; or have wondered how the background radiation that set out on its way at the speed of light when the world was a smaller simpler place is only now reaching us, this book will enlighten you.Even for those whose maths cannot keep up it should be worthwhile, stimulating even, to read the sections at the beginning of each chapter, and those elsewhere light in formulae.For those willing to tackle the exercises he is perhaps a little too generous with the hints. ... Read more

Product Description
Makes a quick, directed thrust through general relativity and black holes.Brings preliminary insights concerning the history and structure of the Cosmos. DLC: General relativity (Physics) ... Read more

Customer Reviews (15)

A nice introduction to General Relativity
This book covers solutions of Einstein's field equations developed in General Relativity, mainly the metric solutions of Schwarzschild, Kerr and Friedmann as well as topics that attracts the general public:GPS, advance of Mercury's perihelion, Einstein Rings and a bit of Cosmology as well (although it's clear the preference of the authors for a closed universe...). It also covers fundamentals of General Relativity with very few math, such as curved space-time, gravitational redshift , equivalence principle of gravity and acceleration, and the author'smasterpiece: The principle of extremal aging .
Don't expect to see any Christoffel symbols, covariant derivative, Ricci tensor, etc. this is a book about solutions, fundamentals and very interesting topics of General Relativity, a very nice way to start studying it!

A Breakthrough in Undergraduate Texts
A book I really wouldn't have thought could have been written. There are a lot of books on general relativity at the superficial level, call these books 'mathless.' There are monumental tomes aimed at the graduate student level, call these books 'tensor calculus.' Here is a book exquisitely positioned between these others. The student will need to have had differential calculus, and perhaps a bit of basic physics, and with these he will get a pretty good, introductory understanding of General Relativity.

The real key to this book is that it explains a lot, but then it open up a bunch of other questions, questions that we really haven't answered yet -- things like dark matter, dark energy, accelerating expansion of the universe, and more.

The book ends with: 'How can physics live up to its true greatness except by a new revolution in outlook which dwarfs all past revolutions? And when it comes, will we not say to each other, Oh, how beautiful and simple it all is! How could we ever have missed it so long.'

That's just the awe, the vision, that we want new and budding physicists to have.

Good book if you like mathematics!
This is the best book about General relativity ( GR ) that I have ever read. Instead of trying to explain GR with words the author is using mathematics to to illustrate some of the consequences of GR. This means that some mathematical knowledge is required ( but not knowledge about tensors and dfferential forms ) and that the reader need to spend some time with paper and pencil to truly understand the text. The examples is concentrated on what is happening around black holes but the advance of Mercury's perihelion and the slowing of light around the Sun is also described. A very good book!

Amazing Introduction to a Very Esoteric Subject
Einstein's general theory of relativity is perhaps one of the most mathematically intense areas of research any physicist or astronomer could undertake.However this book takes the subject and turns it into a joyous romp through curved spacetime.

By avoiding the field equations and focusing on their solutions the authors impart to the eager student an overview of general relativity and set the stage for a more rigorous approach to be undertaken later.This book is the perfect introduction to the subject.

The book is well suited for advanced undergraduates who have had several hours of physics and mathematics.It is likewise suited to serve as a introductory text for graduate students that are studying astrophysics and astronomy.In the latter case the text serves well as an overview of what general relativity is, many of its findings, its predictions, and its relevance to observational astronomy.

If you have a basic understanding of calculus and have studied the special theory of relativity in some detail then this book is well suited to your needs.

Excellent delivery!
This book was delivered in immaculate condition and is exactly how I was hoping it would be. Thank you for your product and i hope to do business with you again!

Sincerely,

Travis ... Read more

Product Description
This book provides an accessible introduction to astronomy and general relativity, aiming to explain the Universe, not just to describe it. Written by an expert in relativity who is known for his clearly-written advanced textbooks, the treatment uses only high-school level mathematics, supplemented by optional computer programs, to explain the laws of physics governing gravity from Galileo and Newton to Einstein. ... Read more

Customer Reviews (7)

Great intro to all advanced topics
There are not a lot of books that come under this category.
This is meant for high school to college students who understand math like trigonometry, some algebra, but no need to know calculus.
The book lays out the graviy topics very well starting from Galilean, Newtonian physics to Einstein's relativity and quantum to some extent.
That is no small feat by any measure.
The market is crammed with two kinds of books. Its either:
a)Popular science books with no maths and throw a bunch of exciting facts at the reader.
b)Advanced Texts with indepth calculus, vectors, riemann geometry, tensors to make sense of the contents

And the author is right-on when he say this in the book.
"this is a book for people who are not afraid to think, who want to understand what gravity is, who want to go beyond the superficial level of understanding that many popular books settle for. But this is also not an advanced texbook. We shall steer a careful middle course between the over-simplification of some popular treatments and the dense complexity of many advanced mathematical texts. This book has equations, but the equations use algebra and (a little) trigonometry, not advanced university mathematics. What is required in place of advanced mathematics is thought"

All in all - an awesome book that I hoped I had when I was in highschool. I have lost count of the books I studied and cross-referenced to get a good understanding of all these topics while in high school.

If you are the person that cannot settle for facts thrown at you by popular science books and cannot deal with advanced calculus math (yet), this book is great for you. Even those with some Calculus background will learn a lot form this book because, the kind of calculus needed to under Riemann surfaces, Maxwell equations, Schrodinger equations, Quantum mechanics is very advanced calculus and vectors. This book can prepare you logically and mentally towards that.

I give two thumbs up to this book

binary stars, neutron stars, black holes
The book was very interesting.I discovered that gravitational waves were predicted by the Special Theory of Relativity and that Einsteins spacetime curvature correctly predicts binary star position and speed and neutron stars.

Matter falling into a neutron star is convert to energy in the form of X-rays at the accretion disk.Neutron stars pull matter into from neighboring stars.The neutron density of the star is constant and does not vary according to size; neutrons, protons and electrons (post big bang temperatures and pressures required); the neutrons can not get any closer.The gravitational pull of a neutron star is 100 trillion times greater than the gravity of the earth.The neutron star emits a strong electro-magnetic wave and strong gravitational waves. How much electricity is the neutron star generating?1 in every 1000 stars in the milky way is a neutron star.Why are neutron stars so common in the Galaxy.Stars between 1.4 and 3 solar masses will, if they supernova , become neutron stars. We see about 2,000 neutron stars and the Milky Way has about 400 billion stars.Neutron stars are spin about 700 times a second with a diameter of 40 km.

Astrophysicist study binary stars more than any other subject. Binary Stars orbits are elliptical and can circle around the perimeter equal distant; or follow elliptical concentric circles pass near each other. Is the binary pulsar PSR 1943+16 orbital distance from it's companion star increasing result of energy loss from radiation and gravity waves?

Too much for amateur scientist
I'm fascinated by gravity.What causes it, how it behaves, how does it relate to quantum mechanics.But for someone other than an advanced (graduate) student, it's too much.The descriptions are all in math, no verbage particularly, except to tell what the math is about.

If you're a graduate student, this is probably an excellent text.But not for the above-average amateur (but well read and knowledgeable) scientist.

Gravity
This is a truly wonderful book. It is suitable for those with little physics and math backgrounds as well as those with more. It is, in fact, incredible how much one can learn here with so little math about topics normally associated with advanced math. In addition to learning many new things, I got great new insights into what I thought I already knew.

I went to this book to learn about general relativity and cosmology. I got that and so much more. The book covers many fascinating topics about the earth, the solar system, galaxies, and brings in physics concepts when they are needed. A recurring theme is the effect of gravity and what resists gravity. So, e.g., white dwarfs are explained by quantum effects resisting complete collapse due to gravity. In addition to learning a lot about general relativity, you get introduced to some aspects of mechanics, statistical mechanics and quantum theory. All this while learning a great deal about astronomy and cosmology.

Calculus isn't required and most of the demonstrations are done with physical arguments, analogies, and simple algebra. Computer programs are available from a website for those who want to use them to illustrate numerical results. (You don't need to use the programs to enjoy the book.) Of course, further study will, at some point, require more math. But this book demonstrates how much can be explained with the simplest concepts, and would be worthwhile for someone to read before getting immersed in the higher math.

A real treasure
How many authors of popular science books begin their books by boasting that they can teach real science to readers who have no math--or no math beyond basic algebra?And then what do you get?Either a tub full of metaphors sloshing about promiscuously or else a math course so compressed it would leave Newton saying, "Duh?"But not in this book.Bernard Schutz takes the reader by the hand and leads him gently on.There is scarcely a bump in the road; yet, by the end of the book, you've not only learned a good deal of physics, astrophysics and cosmology, you've also gotten an inkling of how a physicist thinks.How does Schutz manage to succeed where failure is the rule?Well, partly by magic, I think.But partly by the clever use of simple computer simulations (downloadable for free) and partly by means of a very carefully thought out pedagogical strategy.This gentleman is a teacher par excellence.If you're only going to read one science book in your life, read this one.Just be prepared to spend some time with it. ... Read more

Product Description

Product Description
Einstein's theory of general relativity is a theory of gravity and, as in the earlier Newtonian theory, much can be learned about the character of gravitation and its effects by investigating particular idealized examples. This book describes the basic solutions of Einstein's equations with a particular emphasis on what they mean, both geometrically and physically. New concepts, such as big bang and big crunch-types of singularities, different kinds of horizons and gravitational waves, are described in the context of the particular space-times in which they naturally arise. These notions are initially introduced using the most simple and symmetric cases. Various important coordinate forms of each solution are presented, thus enabling the global structure of the corresponding space-time and its other properties to be analyzed. The book is an invaluable resource both for graduate students and academic researchers working in gravitational physics. ... Read more

Product Description

This book is the result of more than twenty years of lecturing a master course on the General Theory of Relativity at the University of Oslo, Norway, by Dr. Øyvind Grøn. The text has been continuously updated by Dr. Grøn and is written so students can follow the deductions all the way throughout the book. The conceptual content of the general theory of relativity is presented briefly but reasonably and completely. Both bachelor students and master students will find the text useful as the manuscript is organized to easily find the topics one wants to read about, with separate lists of contents, figures, definitions, examples, and an index.

Customer Reviews (1)

Some serious errors in describing the General Relativity!
Quite unfortunately, in this overall well written book the author makes some serious mistakes regarding the essence of the GR. For instance:

1. On the page 10, the author states that in non-inertial
frames the following postulates apply:

"G1. The laws of nature are the same in all reference frames."

"G2. An observer with arbitrary motion may consider himself
to be at rest and the environment as moving."

The both statements, especially G2, are incorrect. An observer
in an accelerated frame definitely can tell that he is
in an accelerated frame, because, for instance, he will be
feeling g-forces, the period of a pendulum will be changing
from the magnitude of the acceleration, etc., quite different
from an inertial (non-accelerated) frame, where everything
will be floating in weightlessness! The correct statement,
describing the equivalence principle is:

"An observer in an uniformly accelerated frame may consider
himself to be at rest in a frame with an uniform gravitational
field. The laws of nature are the same in the both frames."

Since "uniform" gravitational fields do not exist in the
nature (except as an approximation in a very small volume),
Einstein came to the concept of space-time curvature expressing
the "real" gravitational field, etc.

Because of this initial error, on the page 33 the author,
when explaining the (in)famous "twin paradox" concludes
"In order to arrive at a clear answer to these questions,
we shall have to use the result from the general theory
of relativity." This statement is absolutely false, as it
had been shown countless times before in various texts, as
long as the "real" gravitational field is not present
(the Riemann tensor equal to 0), the twin paradox can be
easily resolved using only the special theory of relativity
(see the book by Taylor and Wheeler)! This argument has already
been discussed to death, so it's quite bad to open it anew
in this book :-(
... Read more