Inhomogeneous cosmological models

Cover......Page 1
Frontmatter......Page 2
Contents......Page 8
List of illustrations......Page 12
Preface......Page 14
Acknowledgements......Page 16
1.1 The scope of this review......Page 18
1.2 The sources in the Einstein equations......Page 22
1.3 The FLRW and Kantowski--Sachs limits of solutions......Page 26
1.4 Spherically symmetric perfect fluid spacetimes......Page 33
2.1 The formulae and general properties......Page 36
2.2 Common properties of the two subfamilies......Page 39
2.3 The invariant definitions of the family......Page 40
2.4 Properties of the Szekeres solutions......Page 41
2.5 Common characteristics and comparisons of the two subfamilies of Szekeres solutions......Page 48
2.6 The spherically symmetric and plane symmetric Szafron spacetimes with [GREEK SMALL LETTER BETA][PRIME] =0......Page 57
2.7 The Szafron spacetimes of embedding class 1......Page 62
2.8 Other subcases of the Szafron [GREEK SMALL LETTER BETA][PRIME] =0 spacetime......Page 65
2.9 Stephani\'s (1987) solutions......Page 69
2.10 Other generalizations of various subcases of the [GREEK SMALL LETTER BETA][PRIME] =0 subfamily......Page 72
2.11 Solutions with Kantowski--Sachs geometry and their other generalizations......Page 78
2.12 Solutions of the [GREEK SMALL LETTER BETA][PRIME] [NOT EQUAL TO]0 subfamily with a G3/S2 symmetry......Page 81
2.13 Other subcases of the Szafron [GREEK SMALL LETTER BETA][PRIME] [NOT EQUAL TO]0 spacetime......Page 92
2.14 Electromagnetic generalizations of the solutions of the [GREEK SMALL LETTER BETA][PRIME] [NOT EQUAL TO]0 subfamily......Page 101
2.15 Generalizations of the solutions of the [GREEK SMALL LETTER BETA][PRIME] [NOT EQUAL TO]0 subfamily for viscosity......Page 111
2.16 Other generalizations of the [GREEK SMALL LETTER BETA][PRIME] [NOT EQUAL TO]0 subfamily......Page 114
3.1 Formation of voids in the Universe......Page 117
3.2 Formation of other structures in the Universe......Page 125
3.3 Influence of cosmic expansion on planetary orbits......Page 129
3.4 Formation of black holes in the evolving Universe......Page 131
3.5 Collapse in electromagnetic field......Page 133
3.6 Singularities and cosmic censorship......Page 135
3.7 Influence of inhomogeneities in matter distribution on the cosmic microwave background radiation......Page 141
3.8 Other papers discussing the L--T model......Page 144
3.9 General theorems and considerations......Page 154
4.1 Definition and general properties......Page 159
4.2 The type D solutions......Page 162
4.3 Rediscoveries of the Kustaanheimo--Qvist (K--Q) class of metrics......Page 166
4.4 Invariantly defined subcases of the K--Q class......Page 169
4.5 The McVittie (1967) class......Page 173
4.6 Explicit K--Q solutions corresponding to f(u)=(au2+bu+c)[MINUS SIGN]5/2......Page 174
4.7 Physical and geometrical considerations based on the McVittie (1933) solution......Page 181
4.8 Other solutions of the K--Q class......Page 184
4.9 The conformally flat solutions......Page 185
4.10 The spherically symmetric Stephani solution......Page 188
4.11 Other subcases of the Stephani (1967a) solution......Page 192
4.12 Electromagnetic generalizations of the K--Q spacetimes......Page 196
4.13 Other solutions with charged fluid, related to the Stephani--Barnes family......Page 204
4.14 Generalizations of the Stephani--Barnes models with heat-flow......Page 206
5.2 The energy-momentum tensor of null radiation......Page 212
5.3 The Kerr, Kerr--Newman and Demianski (1972) solutions......Page 214
5.4 The FLRW metrics in null coordinates......Page 217
5.5 Superpositions of the special Demianski (1972) solution with the FLRW backgrounds......Page 218
5.6 Superpositions of the Kerr solution with the FLRW models and other conformally nonflat composites......Page 221
5.7 Conformally flat solutions with null radiation......Page 228
6.1 How to generate a \"stiff fluid\" solution from a vacuum solution......Page 232
6.2 The allowed coordinate transformations......Page 234
6.3 The Einstein equations with a stiff fluid source in an A2-symmetric spacetime......Page 235
6.4 Subcases of the Tomita (1978) class......Page 238
6.5 Electromagnetic generalizations of the stiff fluid spacetimes......Page 241
6.6 Two- and many-fluid generalizations of the stiff fluid spacetimes......Page 243
6.7 Explicit solutions with a stiff perfect fluid source......Page 244
7.1 Other A2-symmetric perfect fluid solutions......Page 255
7.2 A2-symmetric solutions with nonperfect fluid sources......Page 263
7.3 Oleson\'s Petrov type N solutions......Page 264
7.4 Martin and Senovilla\'s (1986a,b) and Senovilla and Sopuerta\'s (1994) solutions......Page 267
7.5 Spherically symmetric solutions with expansion, shear and acceleration......Page 269
7.7 Wainwright\'s (1974) spacetimes and Martin--Pascual and Senovilla\'s (1988) solutions......Page 272
7.8 The anisotropic fluids generated via Kaluza--Klein spaces......Page 277
8.1 Modelling the Universe in relativity......Page 280
8.2 Averaging within approximation schemes......Page 281
8.3 Exact noncovariant averaging......Page 282
8.4 Exact covariant averaging......Page 286
9.1 Afterthoughts......Page 293
Appendix A - Dictionary of abbreviations used in the text and in the diagrams......Page 295
Appendix B - Why should one consider inhomogeneous models of the Universe?......Page 296
Appendix C - Memorable statements about the cosmological principle......Page 301
Appendix D - How was this review compiled?......Page 303
Appendix E - Historical milestones......Page 304
Notes added in proof......Page 307
Bibliography......Page 309
Index......Page 327