Exact Solutions of Einstein's Equations

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A completely revised and updated edition of this classic text, covering important new methods and many recently discovered solutions. This edition contains new chapters on generation methods and their application, classification of metrics by invariants, and treatments of homothetic motions and methods from dynamical systems theory. It also includes colliding waves, inhomogeneous cosmological solutions, and spacetimes containing special subspaces.
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Overview

A completely revised and updated edition of this classic text, covering important new methods and many recently discovered solutions. This edition contains new chapters on generation methods and their application, classification of metrics by invariants, and treatments of homothetic motions and methods from dynamical systems theory. It also includes colliding waves, inhomogeneous cosmological solutions, and spacetimes containing special subspaces.
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Product Details

  • ISBN-13: 9780521230414
  • Publisher: Cambridge University Press
  • Publication date: 2/19/1981
  • Series: Monographs on Mathematical Physics
  • Pages: 448
  • Product dimensions: 5.98 (w) x 8.98 (h) x 1.38 (d)

Table of Contents

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
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