# GENERAL THEORY OF RELATIVITY BOOK

- Contents:

Relativity book. Read reviews from the world's largest community for readers. An accesible version of Einstein's masterpiece of theory, written by th. Relativity: The Special and the General Theory began as a short paper and was eventually published as a book written by Albert Einstein with the aim of giving. From the reviews: "A sophisticated treatment of general relativity with a considerable number of applications to cosmology. The book may be read in several.

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General Theory of Relativity is the generalization of special relativity to include gravitation. It emphasizes that the law of Physics must be same for all observers. The General Theory of Relativity is, as the name indicates, a generalization of the Special Theory of Relativity. It is certainly one of the most remarkable. Book: Relativity: The Special and General Theory. Author: Albert Einstein, – First published: The original book is in the public domain in the.

However the density of exposition in this part might appear a bit steep to a reader without some previous knowledge of differential geometry. Part III deals with Einstein's field equations, and their applications to gravitational waves and black holes. The field equations are derived from a variational principle, the geometrical part Einstein tensor from the Einstein Hilbert action, and the matter part stress energy tensor from a generic action integral for matter.

Various examples of stress energy tensors and in particular, for fluids, are considered, and several are used later in cosmology for instance quintessence and Lorentz invariant vacuum energy. A short chapter on the linear approximation and gravitational waves then follows and it is good to see a section on gravito-electromagnetism.

This part ends with a chapter devoted to black holes which is perhaps the weakest part of the book as it is quite sketchy.

However this is to be expected in a book with an emphasis on cosmology, and such topics are extensively described in other books. The rest of the book parts IV and V is essentially concerned with cosmology. The authors give a detailed description of the applications of the Einstein field equations to a universe with various matter contents, and present in a successful way the recent developments in this domain. The first chapter of part IV describes the standard homogeneous and isotropic cosmological model.

It is followed by an interesting chapter dealing with universes composed of vacuum energy. This chapter ends with sections on cosmic density perturbations, temperature fluctations in the cosmic microwave background and on the history of our universe. It changes your outlook, the way you see the nature and gives you a new and better This book by Dr. It changes your outlook, the way you see the nature and gives you a new and better understanding.

The aim of this book is to introduce people without a strong physics or even scientific background to the special and general theories of relativity - theories that Einstein was the primary developer of. Einstein assumes the reader has passes a "university matriculation exam. I also found basic The aim of this book is to introduce people without a strong physics or even scientific background to the special and general theories of relativity - theories that Einstein was the primary developer of.

I also found basic calculus useful for one section, though it is possible to do without it. For the most part this book is excellent, introducing the minimal amount of mathematics and formal language necessary to understand the most important and fundamental concepts of Einstein's theories in a way that is accessible whilst concise.

It might be possible to do it better with a bigger book, a less formal style and a lot more diagrams but it very interesting to get Einstein's unique perspective as originator of the theories and insight into his thought processes. A few sections are remarkable in contrast with the rest, for being unclear. The section on addition of velocities in special relativity leaves rather more to the reader than anything else in the book, mathematically, and when I looked it up it turned out to be much easier to work out using basic calculus than algebraic division - and the bit that wasn't clear was that a division of two equations was what was required.

This section could be skipped without losing much. The remainder of the muddy sections come at the back end of the section on general relativity.

The simplest precise mathematical formulation of this theory is expressed using tensors - and tensor algebra is way beyond what anybody encounters in standard school maths or physics curricula. Einstein makes no attempt to explain it and in fact never shows the fundamental equation of general relativity.

This makes it very hard for him to explain how gravitational fields and space-time interact, which leads to the lack of clarity in the latter stages of this part of the book.

## See a Problem?

Things get easier and clearer again when he moves on to relativity and cosmology. The final part of the book is a collection of appendices expanding on things discussed earlier on.

I required pen and paper to check the derivation of the Lorentz Transformations from first principles - but this section could just be skipped if the maths bothers you - it doesn't add a lot but it is interesting to see it, if your algebra is up to it. The most rewarding thing for me, since nothing here is completely new to me, was listening to Einstein's voice. He seemed to come at things from a viewpoint much more generally philosophical than most present day physicists would, discussing Kant, Descartes and Hume, for instance.

The section on the concept of "empty space" was fascinating - he concludes that general relativity precludes this notion - one cannot have space-time without it containing "fields. This implies the notion of a field being present even if its magnitude is zero - which is a bizarre concept. Modern quantum mechanics backs these ideas to the hilt and leads me to think that one of the most important areas of inquiry for fundamental physics as it stands is the connection between the classical idea of space-time and the quantum idea of the vacuum.

The fundamental nature of both is obscure - and in some sense they should be the same thing. Overall this is an excellent introduction to special relativity and at least the conceptual underpinnings of general relativity, if not of the full theory, which really just can't be explained properly without knowledge of tensors.

As a kid my serious interests were scientific. I collected feathers, insects, rocks and fossils; maintained an aerospace scrapbook; kept a journal about space exploration; and read a lot of science books ranging from popular stuff and textbooks to serious works from the library which I hardly understood. My greatest intellectual interests by junior high were in cosmology and astronomy.

During middle school, or possibly during the freshman year in high school, I started going to the library to rea As a kid my serious interests were scientific. During middle school, or possibly during the freshman year in high school, I started going to the library to read Einstein. Like many, I thought him the ne plus ultra and believed that mastering his work was of great importance.

Having learned some algebra, trigonometry and geometry in school, I was able to read a little bit of his notation, but not much. Basically, it was beyond me. In high school, starting freshman year, geopolitical concerns started commanding my attention.

I'd been raised under the mushroom cloud like the rest of my generation and we were at war in southeast Asia. History and politics seemed more important, ethically and personally, than science. Sophomore Chemistry sealed the matter. My lab skills were terrible, the teacher was poor, the textbook boring.

That was my last physical science class until a single physics course in college. Being laid off from Loyola and working now only part-time gave me the opportunity to pursue some of the things I'd foregone. So, I picked up Einstein's Relativity, a book he wrote about the relativity theory for the general public. Nov 27, Owlseyes on notre dame, it's so strange a hour blaze and The Times from Nov.

Awesome, see here: The theory of relativity is amazing and important, but contrary to what the tagline says, Einstein himself is probably not the best person to have explain it to you. I read this class for Freshman Studies in college, and I honestly have to admit that I wouldn't have gotten much of it without the significant aid of in-depth lectures and classroom discussions.

This is not because the ideas themselves are too complex, but because Einstein fails in his attempt to make his ideas understood to a layma The theory of relativity is amazing and important, but contrary to what the tagline says, Einstein himself is probably not the best person to have explain it to you. This is not because the ideas themselves are too complex, but because Einstein fails in his attempt to make his ideas understood to a layman. I don't know what book you ought to read instead, but there are certainly many alternatives, of which some must be good.

Einstein does not assume any knowledge of physics, but he does kind of glide over what his variables mean or where they come from, and this makes it hard to grasp what the math means and how it fits in. Mar 18, Heather Cawte rated it it was amazing. Read on my site, free from Project Gutenberg. The biggest problem I had with this was actually one of presentation. The team which had prepared it for release had presented all the equations as jpegs, a reasonable idea when reading it in HTML, but not a good one when reading it on a site!

Still, who am I kidding - the equations probably wouldn't have made sense to me anyway I am an arts graduate trying to understand relativity. I wasn't expecting to understand much, but I was amazed by how much I really did 'get'. Every version of the theory explains it in a slightly different way, and with each version I read, I discover and comprehend a little more. This is by no means an easy read, but it was much more comprehensible than I expected.

## Relativity: The Special and General Theory

It was written for the general public, which certainly helped, and it was an extraordinary experience to be reading such an iconic book and finding that at least some of it made sense Feb 21, Mohamed al-Jamri rated it it was ok. When I was at university the lecturers recommended books on relativity and I even read a few. I gleaned a vague understanding of the subject. None of them recommended Einstein's book. I can't remember where I found it but I'm very glad I did.

It's the best and easiest to understand book about relativity I have ever read. I recommend it to students who are struggling with the concepts and all of them so far have had the "Aha! It's just been returned to me from ano When I was at university the lecturers recommended books on relativity and I even read a few.

It's just been returned to me from another student, and I'm planning to re-read it just for fun. Great book. Not too thick, written well, covers the subject well. If you're at all interested in relativity, this is the book for you. After reading Walter Isaacson's brilliant biography, "Einstein" and finally coming away with an understanding of Einstein's theories, I felt I could make the leap and actually attempt to read something written by the most famous genius of the twentieth century whose theories would transform science and the world.

I chose Einstein's, "Relativity: The Special and General Theory. Well, except for the portions of the book that used mundane objects such as a train, an embankment, Times Square or a clock to describe the most famous theory of all time, the rest of the book a good 60 percent was incomprehensible to me.

It could have just as well been written in Latin. I strongly recommend that unless you have a scientific background, you should not start off by reading this book if you are at all interested in understanding the mind and theories of this, undeniable, genius.

I recommend the Isaacson's book I mentioned above as a good starting point. Not to be deter, I will nevertheless continue my interest in physics and when I have the time and patience I will start reading books about Galileo and Newton's theories, so much seems to have originated from their work.

They are constantly mentioned throughout by Einstein. This year is the centennial of the publication of Einstein's general theory of relativity. I got my hands on the Pi Press edition, which was published 10 years ago coinciding with the centennial of the special theory of relativity.

Yesterday, the New Horizons spacecraft flew past Pluto, sending huge volumes of information back to Earth - and the day before, CERN announced that the LHC has found proof of the existence of the pentaquark. Science continues to reach new frontiers, though nothing t This year is the centennial of the publication of Einstein's general theory of relativity. Science continues to reach new frontiers, though nothing that can compete with the relativity revolution ushered in by Einstein a century ago.

The book also includes an essay by David C. Cassidy titled "The Cultural Legacy of the Relativity Theory" which examines the impact of the theory outside of physics. This proved to be an interesting read and for me it contained lots of new information. On the reception of the theory among the general public he writes: It profoundly challenged the common understanding of everyday physical concepts — space, time, mass, simultaneity.

Even the very name "theory of relativity," coming after the rise of Darwin's theory of evolution, seemed to confirm the decline of old absolute values and beliefs, together with the old world order, and the triumph of a universal relativism. Einstein, of course, objected to such interpretations. Relativity theory had nothing to do with relativism, he insisted. In fact, he had first called it the "theory of invariants," for its emphasis on the unchanging character of natural laws within different reference frames.

It would seem that the real problem was - and still is - the widening gap between specialists and non-specialists; between scientists and the general public. It also helped that this time I knew the disposition of the text and could attack it proceed with more patience.

I also identified what had hampered me so much on the first read: It wasn't quite as daunting this time around. Still, in comparison Gaussian coordinates is a piece of cake.

So when Einstein states the general principle of relativity as "All Gaussian coordinate systems are essentially equivalent for the formulation of the general laws of nature," I feel rather relieved that I can say ok I get that - somehow. Stephen Hawking writes in A Brief History of Time that "seventy years ago, if [Arthur] Eddington is to be believed, only two people understood the general theory of relativity.

Also included in this edition is a commentary by Robert Geroch which provides some useful elucidations expanding on the explanations Einstein uses in the various chapters. Dec 18, Mohamed rated it it was amazing Shelves: How dare I give this masterpiece less than 5 stars?! Although I could hardly claim that I understood 10 percent of the book!

What he was talking about?! Moving reference bodies, Euclidean geometry, Newtonian theory of gravitation, We don't see the real length of things as everything is moving in the space!

Length is relative as well as mass! So what is real?

Is there one single thing that all human can agree on it?! However, the rest of the text is excellent. If you can only read one text in the "advanced" list, it should be Wald. Some topology would be good, the appendix on it is not very extensive.

Pages and pages of calculations. More pages of calculations. This book has derivations of all black hole solutions, geodesic trajectories, perturbations, and more. Not something you would sit down and read for fun. The most cited text in the field. It is absolutely massive and covers so much. Be warned, it's somewhat out-of-date and the notation is generally terrible. The best use for MTW is to look up a result every now and then, there are better books to learn from.

If an exact solution of the Einstein equations was found before , it is in this book and is likely accompanied by a derivation, a sketch of the derivation and some references. Weinberg takes an interesting philosophical approach to GR in this book, and it's not good for an introduction. It was the standard reference for cosmology in the 70s and 80s, and it's not unheard of to reference Weinberg in Texts focused entirely on the geometry of Riemannian and Pseudo-Riemannian manifolds.

These all require knowledge of differential geometry beforehand, save for O'Neil. A very advanced text on the mathematics of Lorentzian geometry. The reader is assumed to be familiar with Riemannian geometry. The sprit of the book is to see how many results from Riemannian geometry have Lorentzian analogues.

The actual applications to physics are speculative. An advanced text on Riemannian geometry, the authors explore the connection between Riemannian geometry and algebraic topology. Many of the concepts and proofs here are used again in Beem and Ehrlich. A terrific introduction to Riemannian geometry. The presentation is leisurely, it's a joy to read. Notable topics covered are global theorems like the sphere theorem.

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A standard introduction to Riemannian geometry. When I don't understand a proof in do Carmo or Jost, I look here. It covers somewhat less material than do Carmo, though they are similar in spirit. A standard high-level introduction to Riemannian geometry. The inclusion of topics like holonomy and analytic aspects of the theory is appreciated. A somewhat standard introduction to Riemannian and pseudo-Riemannian geometry.

Covers a surprising amount of material and is quite accessible. The sections on warped products and causality are very good. Since large parts of the book do not fix the signature of the metric, one can reliably lift many results from O'Neil into GR. A good introduction to general topology and differential topology if you have a strong analysis background.

Most, if not all, theorems of general topology used in GR are contained here. Most of the book is actually algebraic topology, which is not so useful in GR.

A standard introduction to differential topology. Most advanced GR books contain the following: See Steenrod for details. The first three chapters of this text cover manifolds, lie groups, forms, bundles and connections in great detail, with very few proofs omitted. The rest of the book is on functorial differential geometry, and is seriously advanced. That material is not needed for GR.

A somewhat advanced introduction to differential geometry.

Connections in vector bundles are explored in depth. Some advanced topics, like the Cartan-Maurer form and sheaves, are touched upon. Chapter 13, on pseudo-Riemannian geometry, is quite extensive. A very well-written introduction to general differential geometry that doubles as an encyclopedia for the subject.

Most things you need from basic geometry are contained here. Note that connections are not discussed at all. An advanced text on the geometry of connections and Cartan geometries. It provides an alternative viewpoint of Riemannian geometry as the unique modulo an overall constant scale torsion-free Cartan geometry modeled on Euclidean space.

A very rapid and difficult introduction to differential geometry that stresses fiber bundles. Includes an introduction to Riemannian geometry and a lengthy discussion of Chern-Weil theory. A gentle introduction to real analysis in a single variable.

This is a good text to "get your feet wet" before jumping into advanced texts like Jost's Postmodern Analysis or Bredon's Topology and Geometry.

Look here for an intuitive yet rigorous the author is Russian explanation of Lagrangian and Hamiltonian mechanics and differential geometry. This book starts from the basics of linear algebra, and manages to cover a lot of basic math used in physics from a physicist's point of view.

## Relativity

A handy reference. I recommend you those books from the excellent Chicago Physics Bibliography:. Schutz, B. Schutz's book is a really nice introduction to GR, suitable for undergraduates who've had a bit of linear algebra and are willing to spend some time thinking about the math he develops. It's a good book for audodidacts, because the development of the theory is pedagogical and the problems are designed to get you used to the basic techniques.

Come to think of it, Schutz's book is not a bad place to learn about tensor calculus, which is one of the handiest tools in the physics toolkit. Concludes with a little section on cosmology. Dirac, P. You might have heard that Paul Dirac was a man of few words.

Read this book to find out how terse he could be. It develops the essentials of Lorentzian geometry and of general relativity, up through black holes, gravitational radiation, and the Lagrangian formulation, in a blinding 69 pages! I think this book grew out of some undergrad lectures Dirac delivered on GR; they are more designed to show what the hell theory is all about than to teach you how to do calculations.

I actually didn't like them all that much; they were a little too dry for my taste. It's amusing though, to put Dirac's book next to the book of Misner, Thorne, and Wheeler.

D'Inverno, R. I think that D'Inverno is the best of the undergraduate texts on GR an admittedly small group. It's a tad less elementary than Schutz, and it has a lot more detail and excursions into interesting topics.

I seem to remember that it's development of necessary mathematics struck me as somehow lacking, but unfortunately I don't remember what exactly annoyed me. But for physics, I don't think you can beat it. Just be careful: Misner, C. Gravitation has a lot of nicknames: It's over a thousand pages in length, and probably weighs about 10 pounds.

It makes a very effective doorstop, but it would be a shame to use it as one. I'm not sure I'd recommend it for first time downloaders, but after you know a little about the theory, it's about the most detailed, lucid, poetic, humorous, and comprehensive exposition of gravity that you could ask for.

MTW is laden with stories and quotations.

Oh yes. The theory of general relativity is all laid out in loving detail. You will not find a better explanation of the physics of gravitation anywhere. Well, sorta. MTW is a little out of date. MTW is good for the basics, but there's actually been quite a bit of work done in GR since it's publication in See Wald for details. Wald, R. My favorite book on relativity.

Wald's book is elegant, sophisticated, and highly geometric. That's geometric in the sense of modern differential geometry, not in the sense of lots of pictures, however.

If you want pictures, read MTW. Fortunately, his exposition is very clear and supplemented by good problems. After he's introduced Einstein's equation, he spends some time on the Schwarzchild and Friedman metrics, and then moves on into a collection of interesting advanced topics such as causal structure and quantum field theory in strong gravitational fields.

Stewart, J.

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Stewart's book is often for sale at Powell's, which is why I've included it in this list. It's coverage of differential geometry is very modern, and useful if you want some of the flavor of modern geometry. But it's topics are all covered in Wald's book and more clearly to boot. I've been trying to teach myself GTR for about the last twelve months. They're on YouTube but there's a general link here http: I find all of the textbooks hard going! I bought Lambourne after spending a lot of time trying to understand Schutz, which is quite rigorous enough for me and a good reference book for my level.

He takes you through the maths quite carefully, but it's not easy and big chunks go straight over my head. I liked it enough to download a copy though. I bought D'Inverno second hand but I wish I hadn't bothered. Much too difficult, though I do occasionally look at it.

Carroll has put a complete course of notes online as well. See http: You might also want to take a look at A Most Incomprehensible Thing: According to the blurb:. This book is aimed at the enthusiastic general reader who wants to move beyond the maths-lite popularisations in order to tackle the essential mathematics of Einstein's fascinating theories of special and general relativity The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Schwarzschild solution; simple black holes and what different observers would see if someone was unfortunate enough to fall into one.

Also covered are the mysteries of dark energy and the cosmological constant; plus relativistic cosmology, including the Friedmann equations and Friedmann-Robertson-Walker cosmological models.

To have fun while reading these books, you can enjoy "The Einstein Theory of Relativity:I wasn't expecting to understand much, but I was amazed by how much I really did 'get'. After the rise of the Nazi party, Einstein made Princeton his permanent home, becoming a U.

Besides the overall "mathematical" presentation, notable features are a discussion of the Lovelock theorem, gravitational lensing, compact objects, post-Newtonian methods, Israel's theorem, derivation of the Kerr metric, black hole thermodynamics and a proof of the positive mass theorem.

While still appreciating Einstein's visual demonstrations and thought experiments, I wouldn't have minded a few more equations and formulas either, to combine the powers of intuition and precision. Relativity and the Problem of Space Bibliography Index.

I read this class for Freshman Studies in college, and I honestly have to admit that I wouldn't have gotten much of it without the significant aid of in-depth lectures and classroom discussions. If you want pictures, read MTW.

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