teaches calculations, some statements without justification

books:


	• Exploring Black Holes: Introduction to General Relativity Edwin F. Taylor, John Archibald Wheeler Benjamin Cummings, 2000 - 352 pages average customer review:based on 14 reviews view larger image
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highly recommended

Terrific - but not easy

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.

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Just wonderful!

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.

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teaches calculations, some statements without justification

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.

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A Great Achievement.

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 -- an intuitive understanding. 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 paradigm book next. Gentlemen, kudos in the highest!

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well worth it

this is a nice book that allows one to approach general realtivity with somewhat rusty math. One should read the special relativty book by the same authors first though.

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