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Exact Solutions of Einstein's Field Equations
monograph
Author(s):
Hans Stephani
,
Dietrich Kramer
,
Malcolm MacCallum
,
Cornelius Hoenselaers
,
Eduard Herlt
Publication date
(Online):
2009
Publisher:
Cambridge University Press
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There is no author summary for this book yet. Authors can add summaries to their books on ScienceOpen to make them more accessible to a non-specialist audience.
Related collections
Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory
Author and book information
Book
ISBN:
9780511535185
Publication date (Print):
2003
Publication date (Online):
2009
DOI:
10.1017/CBO9780511535185
SO-VID:
d6c55bfc-3714-422e-aa1c-7838c26998e7
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Book chapters
pp. xix
Preface
pp. xxvii
Notation
pp. 1
Introduction
pp. 9
Differential geometry without a metric
pp. 30
Some topics in Riemannian geometry
pp. 48
The Petrov classification
pp. 57
Classification of the Ricci tensor and the energy-momentum tensor
pp. 68
Vector fields
pp. 75
The Newman–Penrose and related formalisms
pp. 91
Continuous groups of transformations; isometry and homothety groups
pp. 112
Invariants and the characterization of geometries
pp. 129
Generation techniques
pp. 157
Classification of solutions with isometries or homotheties
pp. 171
Homogeneous space-times
pp. 183
Hypersurface-homogeneous space-times
pp. 210
Spatially-homogeneous perfect fluid cosmologies
pp. 226
Groups G3 on non-null orbits V2. Spherical and plane symmetry
pp. 247
Spherically-symmetric perfect fluid solutions
pp. 264
Groups G2 and G1 on non-null orbits
pp. 275
Stationary gravitational fields
pp. 292
Stationary axisymmetric fields: basic concepts and field equations
pp. 304
Stationary axisymmetric vacuum solutions
pp. 319
Non-empty stationary axisymmetric solutions
pp. 341
Groups G2I on spacelike orbits: cylindrical symmetry
pp. 358
Inhomogeneous perfect fluid solutions with symmetry
pp. 375
Groups on null orbits. Plane waves
pp. 387
Collision of plane waves
pp. 407
The various classes of algebraically special solutions. Some algebraically general solutions
pp. 416
The line element for metrics with k = σ = 0 = R11 = R14 = R44, Θ +iω ≠ 0
pp. 422
Robinson–Trautman solutions
pp. 437
Twisting vacuum solutions
pp. 455
Twisting Einstein–Maxwell and pure radiation fields
pp. 470
Non-diverging solutions (Kundt's class)
pp. 485
Kerr–Schild metrics
pp. 506
Algebraically special perfect fluid solutions
pp. 518
Application of generation techniques to general relativity
pp. 553
Special vector and tensor fields
pp. 571
Solutions with special subspaces
pp. 580
Local isometric embedding of four-dimensional Riemannian manifolds
pp. 605
The interconnections between the main classification schemes
pp. 615
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