Exact Solutions of Einstein's Field Equations / Edition 2

Exact Solutions of Einstein's Field Equations / Edition 2

by Hans Stephani, Dietrich Kramer, Malcolm MacCallum, Cornelius Hoenselaers
     
 

ISBN-10: 0521461367

ISBN-13: 9780521461368

Pub. Date: 03/28/2003

Publisher: Cambridge University Press

"A revised edition of the now classic text, Exact Solutions of Einstein's Field Equations gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It starts by introducing the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find…  See more details below

Overview

"A revised edition of the now classic text, Exact Solutions of Einstein's Field Equations gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It starts by introducing the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties." This edition has been expanded and updated to include the new developments in the field since the publication of the first edition. It contains five completely new chapters, covering topics such as generation methods and their application, colliding waves, classification of metrics by invariants and inhomogeneous cosmologies. It is an important source and guide for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. Parts of the book can also be used for preparing lectures and as an introductory text on some mathematical aspects of general relativity.

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Product Details

ISBN-13:
9780521461368
Publisher:
Cambridge University Press
Publication date:
03/28/2003
Series:
Cambridge Monographs on Mathematical Physics Series
Edition description:
REV
Pages:
732
Product dimensions:
6.85(w) x 9.72(h) x 1.57(d)

Table of Contents

Preface
List of tables
Notation
1Introduction1
Pt. IGeneral methods9
2Differential geometry without a metric9
3Some topics in Riemannian geometry30
4The Petrov classification48
5Classification of the Ricci tensor and the energy-momentum tensor57
6Vector fields68
7The Newman-Penrose and related formalisms75
8Continuous groups of transformations; isometry and homothety groups91
9Invariants and the characterization of geometries112
10Generation techniques129
Pt. IISolutions with groups of motions157
11Classification of solutions with isometries or homotheties157
12Homogeneous space-times171
13Hypersurface-homogeneous space-times183
14Spatially-homogeneous perfect fluid cosmologies210
15Groups G[subscript 3] on non-null orbits V[subscript 2]. Spherical and plane symmetry226
16Spherically-symmetric perfect fluid solutions247
17Groups G[subscript 2] and G[subscript 1] on non-null orbits264
18Stationary gravitational fields275
19Stationary axisymmetric fields: basic concepts and field equations292
20Stationary axisymmetric vacuum solutions304
21Non-empty stationary axisymmetric solutions319
22Groups G[subscript 2]I on spacelike orbits: cylindrical symmetry341
23Inhomogeneous perfect fluid solutions with symmetry358
24Groups on null orbits. Plane waves375
25Collision of plane waves387
Pt. IIIAlgebraically special solutions407
26The various classes of algebraically special solutions. Some algebraically general solutions407
27The line element for metrics with [kappa] = [sigma] = 0 = R[subscript 11] = R[subscript 14] = R[subscript 44], [actual symbol not reproducible]416
28Robinson-Trautman solutions422
29Twisting vacuum solutions437
30Twisting Einstein-Maxwell and pure radiation fields455
31Non-diverging solutions (Kundt's class)470
32Kerr-Schild metrics485
33Algebraically special perfect fluid solutions506
Pt. IVSpecial methods518
34Application of generation techniques to general relativity518
35Special vector and tensor fields553
36Solutions with special subspaces571
37Local isometric embedding of four-dimensional Riemannian manifolds580
Pt. VTables605
38The interconnections between the main classification schemes605
References615
Index690

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