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| Preface | ||
| List of tables | ||
| Notation | ||
| 1 | Introduction | 1 |
| Pt. I | General methods | 9 |
| 2 | Differential geometry without a metric | 9 |
| 3 | Some topics in Riemannian geometry | 30 |
| 4 | The Petrov classification | 48 |
| 5 | Classification of the Ricci tensor and the energy-momentum tensor | 57 |
| 6 | Vector fields | 68 |
| 7 | The Newman-Penrose and related formalisms | 75 |
| 8 | Continuous groups of transformations; isometry and homothety groups | 91 |
| 9 | Invariants and the characterization of geometries | 112 |
| 10 | Generation techniques | 129 |
| Pt. II | Solutions with groups of motions | 157 |
| 11 | Classification of solutions with isometries or homotheties | 157 |
| 12 | Homogeneous space-times | 171 |
| 13 | Hypersurface-homogeneous space-times | 183 |
| 14 | Spatially-homogeneous perfect fluid cosmologies | 210 |
| 15 | Groups G[subscript 3] on non-null orbits V[subscript 2]. Spherical and plane symmetry | 226 |
| 16 | Spherically-symmetric perfect fluid solutions | 247 |
| 17 | Groups G[subscript 2] and G[subscript 1] on non-null orbits | 264 |
| 18 | Stationary gravitational fields | 275 |
| 19 | Stationary axisymmetric fields: basic concepts and field equations | 292 |
| 20 | Stationary axisymmetric vacuum solutions | 304 |
| 21 | Non-empty stationary axisymmetric solutions | 319 |
| 22 | Groups G[subscript 2]I on spacelike orbits: cylindrical symmetry | 341 |
| 23 | Inhomogeneous perfect fluid solutions with symmetry | 358 |
| 24 | Groups on null orbits. Plane waves | 375 |
| 25 | Collision of plane waves | 387 |
| Pt. III | Algebraically special solutions | 407 |
| 26 | The various classes of algebraically special solutions. Some algebraically general solutions | 407 |
| 27 | The line element for metrics with [kappa] = [sigma] = 0 = R[subscript 11] = R[subscript 14] = R[subscript 44], [actual symbol not reproducible] | 416 |
| 28 | Robinson-Trautman solutions | 422 |
| 29 | Twisting vacuum solutions | 437 |
| 30 | Twisting Einstein-Maxwell and pure radiation fields | 455 |
| 31 | Non-diverging solutions (Kundt's class) | 470 |
| 32 | Kerr-Schild metrics | 485 |
| 33 | Algebraically special perfect fluid solutions | 506 |
| Pt. IV | Special methods | 518 |
| 34 | Application of generation techniques to general relativity | 518 |
| 35 | Special vector and tensor fields | 553 |
| 36 | Solutions with special subspaces | 571 |
| 37 | Local isometric embedding of four-dimensional Riemannian manifolds | 580 |
| Pt. V | Tables | 605 |
| 38 | The interconnections between the main classification schemes | 605 |
| References | 615 | |
| Index | 690 |
| Price | Condition | Delivery | Seller | Action |
| $199.00 | Digital |
| WonderClub |
James Keene
reviewed Exact Solutions to Einstein's Field Equations (Cambridge Monographs on Mathematical Physics Series) on April 04, 2012
Exact Solutions to Einstein's Field Equations
This is some very impressive stuff.
I've read a lot of nonfiction science books that sometimes had equations but mostly did not, but what I really wanted was a cohesive drive, an arrow to spear right through some of the biggest questions of our time... such as What Is Time.
Sean Carroll manages to keep things very sharp between what is perfectly understood and all of the theories that are somewhat understood, and the other Cosmology stuff that's mostly just baffling. :)
Any way you look at it, though, this is not a book that gets derailed or goes off into super strange directions. He lays out all the foundations, from the opening definitions of Time and what we think it means, from the average to the rather advanced notions of space-time and curvature, Einstein's energy equation, speed of light, diliation, moving all the way to Black Holes. This is very solid stuff.
Plus, we have a very coherent definition of Time as Entropy, showing us just how complicated it can get when time's arrow might just be the illusion that Hawking says it is. I really enjoyed that discussion.
Of course, we come up with lots of possibilities and digressions that are always explored in SF, too, but most of these are just bylines, moving quickly by the Grandfather paradox, etc, to get right back on the main track.
Yes. We have Equations. :) Fortunately, the author does a very good job about explaining them and even getting deeper into the extra areas that made this rather more interesting for me since I've read many science books and have heard most of this already.
I recommend this for anyone interested in Time. :) Not time management. Just Time. :) We do touch rather heavily upon Cosmology by the end, too, which was a blast and a half, getting into many-universes theory and string theory, to name a few. And he makes it clear! :)
Seriously. This was some sharp stuff. Very readable. It's not a general overview. You might say it's putting time's arrow right through the heart of a big question and staying on track all the way to the end.
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