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Introducing Einstein's Relativity Introducing Einstein's Relativity
by Ray D'Inverno

383 pages
Level: advanced undergraduate text book

The mathematics of General Relativity

There are many things that I like about D'Inverno's "Introducing Einstein's Relativity" although it failed to meet my expectations at least as an introductory text to Einstein's theory of relativity. This is too bad, because the author has gone to great lengths to make the material as accessible as possible. He has divided the book into a relatively large number of chapters and sub-chapters so that the student is not overwhelmed with the amount of material. "Introducing Einstein's Relativity" is heavily illustrated and the layout is aesthetically pleasing. The writing is straightforward and clear. D'Inverno even includes "a final note for the less able student" to encourage those of us who find the material difficult.

He does introduce vectors with the old fashioned coordinate approach which I personally find more difficult then the modern way, but the real problem with "Introducing Einstein's Relativity" is that it is simply too advanced to be an "introduction".

Here is what D'Inverno lists as the prerequisites: "On the mathematical side you need to know calculus, up to and including partial differentiation, and solution of simple ordinary differential equations. Basic algebra is assumed and some matrix theory, although you can probably take eigenvalues and diagonalisation on trust. Familiarity with vectors and some exposure to vector fields is assumed. It would also be good to have met the ideas of a vector space and bases. We use Taylor' theorem a lot, but probably knowledge of Maclaurin's will be sufficient. On the Physics side, you obviously need to know Newton's laws and Newtonian gravitation.

It would be helpful also to know a little about the potential formulation of gravitation (though, again, just the basics will do). The book assumes familiarity with electromagnetism (Maxwell's equations, in particular) and fluid dynamics (the Navier-Stokes equation, in particular), but neither of these are absolutely essential. It would be very helpful to have met some ideas about waves (such as the fundamental relationship c = wave-length * frequency) and the wave equation in particular. In cosmology, it is assumed that you know something about basic astronomy.

The main problem is that D'Inverno, maybe in enthusiasm for his subject, simply tries to pack too much in. He does indicate certain sections which can be skipped over, but there is a great deal of material such as the Lie Derivative that could have been better put off to a second volume. Strangely enough in the section on further reading D'Inverno recommends various books for a first course in general relativity.

While I can not recommend "Introducing Einstein's Relativity" as an introduction to relativity, it certainly has a great of useful material for the more advanced student. I'm looking forward to using it when I become one.
Review by Ed Ehrlich
Table Of Contents

Overview

1. The Organization of the book

Part A. Special Relativity
2. The k-calculus
3. The key attributes of special relativity
4. The elements of relativistic mechanics

Part B. The Formalism of Tensors

5. Tensor algebra
6. Tensor calculus
7. Integration, variation, and symmetry

Part C. General Relativity
8. Special relativity revisited
9. The principles of general relativity
10. The field equations of general relativity
11. General relativity from a variational principle
12. The energy-momentum tensor
13. The structure of the field equations
14. The Schwarzschild solution
15. Experimental tests of general relativity

Part D. Black Holes
16. Non-rotating black holes
17. Maximal extension and conformal compactification
18. Charged black holes
19. Rotating black holes

Part E. Gravitational Waves
20. Plane gravitational waves
21. Radiation from an isolated source

Part F. Cosmology
22. Relativistic cosmology
23. Cosmological modes

Answers to exercises

Further reading

Selected bibliography

Index

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