Customer Reviews

Exploring Black Holes: Introduction to General Relativity

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'Exploring Black Holes' was meant for me. I'm 54 years old andhave spent the last 3 years learning some mathematics with a goal of learning more than just the concepts of General Relativity. My math skills leave me in the group Professors Edwin F. Taylor and John Archibald Wheeler are trying to reach with 'Exploring Black Holes'. The purpose behind Professors Taylor and Wheeler writing the book is explicitly stated in the 'The Author, Edwin F. Taylor' and 'Back Cover Copy' sections for 'Exploring Black Holes' located at Amazon.com. My purpose in writing this review is to point out that 'Exploring Black Holes' is not just for university students but is also a very effective tool which can be used for 'self study'. Used by folks such as myself. Terms and methods are clearly defined eliminating the need to search for explanations outside the text of 'Exploring Black Holes'. Step by step example problems are provided to insure problem solving can be achieved through self study and the text is 'fun' to read...I sincerely recommend 'Exploring Black Holes' as a self study introduction to General Relativity and I would like to thank Professors Taylor and Wheeler for making this unique approach available. Sincerely Yours Bruce Pew

This book is different from every other introduction to general relativity I know. And better. The eminent authors connect geometry directly to physics, bypassing tensors. Curvature in space is detected by very simple length measurements; curvature in time, by the lengthening of periods of oscillations. There are nuggets in almost every page. I loved the demonstration that you don't really need coordinates to describe geometry: the shape of a boat is reconstructed entirely in terms of distances. Their dynamical principle is the maximum proper time principle. The way they derive energy and momentum from this principle is sterling physics. You'll learn a lot of general relativity in this book. Not all of it. But, learning to love it, you'll learn the advanced topics that cannot be treated this way by yourself, in other books. Perhaps in the huge Misner, Thorne, Wheeler.

I am a graduate student in physics and I like reading books for undergraduates like this one. I've learned more from this book than from the 'bible' MTW or from the usual superficial graduate courses in GR that boil down to 'index gymnastics' whithout conceptual depth.

The dominant theme in the book is spherically symmetric noncharged and nonrotating black holes described by the Schwartzschild metric. Only the last two projects deal with rotating black holes and cosmological metrics. The book covers only a small application chapter of GR so don't expect to see the Einstein equations or tensors (there isn't a single one).

It took me a month to read the book and do all the exercises which I found easy most of the time since they come with pretty detailed instructions how to solve them. You will need to know a little special relativity and calculus so it is completely within the reach of an undergrad. Also the authors prefer to work directly with the differentials in the metric instead of using 4-vectors, scalar producst and components - that is more natural for most beginners. You can see the 4-vector approach in more advanced books (still for beginners) like James Hartle's "Introduction to general relativity".

The Schwartzschild metric is stated without derivation. Then you are introduced to 3 different observers around the black hole and their measurements. You will use a variational principle called in the book 'Principle of extremal aging', to derive the orbits of bodies and light rays around the black hole and constants of motion like energy and angular momentum. The radial motion is tackled through 'effective potential', the angular motion through the angular momentum.

At the end of the book you will begin to understand how to tackle a general metric: how to interpret its coordinates in terms of measurements performed by different observers, how the constants of motions are connected to symmetries in the metric, how to get the constants of motion with the variational principle and so on...

Besides all that, you will learn a bunch of wonderfull facts about black holes that will make you a star at a nerd's party :) Can you cross the horizon and what is seen by different observers, the time from the moment your body feels uncomfortable till the moment you reach the center of the black hole, how the night sky looks close to the black hole and so on.

Some of the projects in the book calculate the hystorical experimental proofs of GR: bending of light near sun, precession of mercury's orbit and so on. The projects contain queries that you have to fill in reading the text. The solutions of these are usually shorter than the questions themselves :)

My only objection is that sometimes the book makes statements without justification. For example, it is enogh to say that the principle of extremal aging like every principle is a statement in agreement with the experiment that can't be proven, we just know it works but don't know why. Instead of explaining that, the book states the principle several times wasting paper to my opinion and you still don't understand where that principle comes from. Repeating statements without proper explanation is equivalent to brain-washing and just makes the text unnecessary bulky and inefficient.

UPDATE for the authors [6 Nov 2007]: What I meant with the above paragraph is that while the 'principle of extremal aging' can be shown to follow from the assumptions/axioms in the context of Special Relativity (like in the twin paradox), in GR it is postulated by analogy, not proven. Sections 3.1 and 3.2 illustrate the principle but are not explicit enough about its origin in GR.

For sins like that I gave it 4/5. Keep in mind I am a pretty demanding reader and I give 5/5 only to masterpieces like some books of David Griffiths where you can see the authour applied great effort to streamline the logic and clearly justify it to the reader.

This book fills in a very important gap in physics texts. The gap is between popular books on modern physics that seem to think readers are terrified of equations and those books that are extremely mathematical and require the reader to understand tensor analysis and differential geometry in order to work with Einstein's field equation. This book fits perfectly in between and provides an excellent introduction to relativity and black holes while only using algebra and elementary calculus. It contains excellent chapter problems and some really great application chapters (such as relativistic effects in the GPS system, etc.). The book only works with the metrics of the field equations thus simplifying the math greatly. This book can serve as an excellent stepping stone to the more advanced books such as MTW or a great book for someone just looking to understand the details of relativity better than can be done with the popular layperson books. Extremely interesting book and I am enjoying it tremendously! My only complaint (and this is very minor) is that the authors attempt to be "cute" from time to time and I personally don't like "cute" books. However, overall just about the best book purchase I've made in awhile (and I make alot)!

I have not yet finished reading this book but my excitement over its brilliance forces me to comment. This book is shear magic in its ability to explain very difficult and strange phenomena in an intuitive and simple way. I have read the authors' book SpaceTime Physics as well as GR by Schutz and can do the tensors and all that; yet I am in awe of the ability these authors have of succeding at the near impossible. Using the study of black holes as the motivation for GR study is perfect. I love the choice of the variational principle to cut to the heart of the math. I recommend this book to anyone for self-study who has a smattering of calculus (not much is really needed). I am looking forward to studying Kip Thorne's membrane paradign book next. Gentlemen, kudos in the highest!

I am extremely impressed by what Taylor and Wheeler are able to do in this book! I have wanted for some time to offer a course at approximately the sophomore level that would include a thorough treatment of special relativity, but would also delve non-trivially into general relativity. Given that general relativity usually demands at least a full semester by itself, and requires that a fair amount of time be spent motivating and developing tensor analysis, this would seem to be an impossible goal. Exploring Black Holes now makes this a real possibility, and gives students a chance to see what GR is really about without getting lost in the mathematics.

I found the book to be extremely clearly written, and quite understandable; I hope my students this fall will agree.

Finally, I was very pleasantly surprised by the modest price (for this hardcover book). I am sure my students will be grateful, since they need to purchase another text as well to cover special relativity.

As other reviewers have said, Taylor and Wheeler accomplish something marvelous (and by conventional wisdom impossible), making a non-trivial portion of general relativity accessible to physics undergraduates. But be warned that "accessible" does not mean easy! A good background in special relativity is essential, for example from the authors' earlier book Spacetime Physics. Beyond that, readers must be prepared for convoluted reasoning and heavy duty algebra in some parts of the book, covering the more esoteric optical effects of black holes and the effects of rotation. It was an effort for me to get through this book - but well worth it.

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.

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!

This book sidesteps the hard work needed to motivate and develop the Einstein field equations, and goes directly to one of the most important solutions of the equations, the Schwarzschild solution, which gives rise to the concept of a black hole. By exploring what observers in different parts of space-time would experience along their different trajectories (whether falling into a black hole or watching from a safe spot far away), Taylor and Wheeler manage to convey an intuitive understanding for such typical GR "paradoxes" such as the fact that the same "event" (the crossing over of an object through the event horizon) can be seen to take 15 minutes, or forever, depending on who's watching it.

Because of what it omits, this book is not a complete presentation of GR. It does present the most fun part of GR, however, in a way that is mathematically accessible.

Along the way, a few side questions are adddressed, like "How painful would it be to be squished/torn apart as I fall into a black hole?" A lot of time is also spent explaining how the weird trajectories of light within the event horizon will transmogrify what is seen by the observer.

This is a great book and a lot of fun. I am also left with a greater motivation to go back to a more complete presentation, to be convinced that "this is where you have to end up". Although much longer, this book is a worthy successor to the original output of this dynamic duo, "Spacetime Physics".