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Tables of Contents for The Large Scale Structure of Space-Time
Chapter/Section Title
Page #
Page Count
Preface
xi
The role of gravity
1
9
Differential geometry
10
46
Manifolds
11
4
Vectors and tensors
15
7
Maps of manifolds
22
2
Exterior differentiation and the Lie derivative
24
6
Covariant differentiation and the curvature tensor
30
6
The metric
36
8
Hypersurfaces
44
3
The volume element and Gauss' theorem
47
3
Fibre bundles
50
6
General Relativity
56
22
The space--time manifold
56
3
The matter fields
59
5
Lagrangian formulation
64
7
The field equations
71
7
The physical significance of curvature
78
39
Timelike curves
78
8
Null curves
86
2
Energy conditions
88
8
Conjugate points
96
6
Variation of arc-length
102
15
Exact solutions
117
63
Minkowski space--time
118
6
De Sitter and anti-de Sitter space--times
124
10
Robertson--Walker spaces
134
8
Spatially homogeneous cosmological models
142
7
The Schwarzschild and Reissner--Nordstrom solutions
149
12
The Kerr solution
161
7
Godel's universe
168
2
Taub--NUT space
170
8
Further exact solutions
178
2
Causal structure
180
46
Orientability
181
1
Causal curves
182
4
Achronal boundaries
186
3
Causality conditions
189
12
Cauchy developments
201
5
Global hyperbolicity
206
7
The existence of geodesics
213
4
The causal boundary of space-time
217
4
Asymptotically simple spaces
221
5
The Cauchy problem in General Relativity
226
30
The nature of the problem
227
1
The reduced Einstein equations
228
3
The initial data
231
2
Second order hyperbolic equations
233
11
The existence and uniqueness of developments for the empty space Einstein equations
244
5
The maximal development and stability
249
5
The Einstein equations with matter
254
2
Space--time singularities
256
43
The definition of singularities
256
5
Singularity theorems
261
15
The description of singularities
276
8
The character of the singularities
284
5
Imprisoned incompleteness
289
10
Gravitational collapse and black holes
299
49
Stellar collapse
299
9
Black holes
308
15
The final state of black holes
323
25
The initial singularity in the universe
348
17
The expansion of the universe
348
11
The nature and implications of singularities
359
6
Appendix A: Translation of an essay
365
4
P.S. Laplace
Appendix B: Spherically symmetric solutions and Birkhoff's theorem
369
4
References
373
8
Notation
381
4
Index
385