Proc. 2nd Samos meeting on cosmology, geometry and relativity

Preface......Page 1
Contents......Page 3
Introduction......Page 4
1 Definitions......Page 5
2 Wave Maps. Cauchy Problem......Page 6
3 Local Existence Theorem. Global Problem......Page 10
4 First Energy Estimate......Page 13
5 Second Energy Estimate......Page 16
6 Case of $n leq 3$......Page 20
8 Case $n = 1$......Page 23
9 Case $n = 2$......Page 24
1 First Energy Estimate......Page 25
2 Second Energy Estimate......Page 27
3 Global Existence Theorem......Page 29
References......Page 31
1 Introduction......Page 33
2 Every Time Slicing Is ``Harmonic''......Page 37
3 Canonical Action and Equations of Motion......Page 38
4 Contracted Bianchi Identities......Page 42
5 Wave Equation for $K_{i j}$......Page 43
6 Einstein-Bianchi Hyperbolic System......Page 45
7 Einstein-Christoffel System......Page 48
8 Conformal ``Thin Sandwich'' Data for the Initial Value Problem......Page 50
References......Page 54
1 Introduction......Page 58
2 The Gauss  law constraint of electromagnetism......Page 60
3 The momentum constraint......Page 63
4 Boosting a single black hole......Page 68
5 More general initial-data sets with punctures......Page 70
References......Page 71
1 Introduction, Notation, and Background......Page 74
2 Some Mathematical Background......Page 79
2.1 The Teichm{accent 127 u}ller Space of Conformal Structures newline of a Manifold......Page 80
2.2 The Yamabe Type of a Manifold......Page 82
2.3 Some $3$-Manifold Topology......Page 83
2.4 Conformal Geometry and the $ sigma $-Constant......Page 84
3 Properties of the Reduced Hamiltonian......Page 88
4 Proofs of the Properties of $H_{rm {reduced}}$......Page 90
5 The Infimum of $H_{rm {reduced}}$ newline and Its Relation to the $sigma $-Constant of $M$......Page 97
6 Concluding Remarks......Page 98
References......Page 102
1 Introduction......Page 105
2 M-Theory......Page 106
2.2 Symmetry Enhancement......Page 107
2.4 Three-Branes and Cosmology......Page 108
3.1 The Classical Solution......Page 109
3.3 Supersymmetries......Page 110
3.4 Vacuum Interpolation, Conformal Flatness and Couch-Torrence Symmetry......Page 111
4 $AdS_{p+2}$ and Its Horospheres......Page 112
5 Covering Spaces, the Eternal Return and Wrapping in Time......Page 114
6 $AdS_{p+2}$ as a Solvable Group Manifold......Page 116
6.1 The Iwasawa Decomposition......Page 117
6.2 Symmetric Space Duality, the Anti-Hopf Fibration  and the Goedel Viewpoint......Page 118
6.4 Horospheric Brane-Waves......Page 120
7 Conformal Compactifications and the Boundary of $AdS_{p+2}$......Page 121
7.1 Conformally Compactified Minkowski Spacetime......Page 122
7.3 The Conformal Boundary of $H^{p+1}$ and the Doppelganger on the Other Sheet......Page 124
8 The Geodesic Flow on AdS and the Future Tube of the Boundary......Page 126
9 The Anti-de-Sitter Algebra and Quantized Energies......Page 130
10 CFT & ESU {accent 18 a} la L{accent 127 u}scher and Mack......Page 132
10.2 Singletons......Page 134
11 Finite Temperatures and Event Horizons with Exotic Topology......Page 135
11.1 Three Kinds of Static Metric......Page 136
11.2 Tachyonic Black Holes......Page 137
12 Concluding Observations......Page 138
12.1 Nonlinear Realisations and Spontaneous Symmetry Breaking......Page 139
12.2 Anti-de-Sitter Space as a Moduli Space......Page 140
12.4 Strings in Four Dimensions......Page 142
References......Page 143
1 Introduction......Page 146
2.1 Coordinates......Page 149
2.2 Isometries and Geodesics......Page 155
2.3 Identifications......Page 158
2.4 Multiple Black Holes......Page 161
2.5 Other Topologies......Page 168
3 Time Development......Page 171
3.1 Fixed Points at Infinity......Page 175
4 Angular Momentum......Page 176
4.2 Does It Rotate?......Page 178
4.3 Multiple Black Holes with Angular Momentum......Page 179
5 Conclusions......Page 180
References......Page 181
S.W. Hawking......Page 183
1 Introduction......Page 194
2.1 Horizon Methods......Page 199
2.2 Causal Structure Methods......Page 204
2.3 Topological Questions......Page 206
3 Mapping Methods......Page 208
3.1 Ernst Representation of the $T^3$ Gowdy Models......Page 209
3.2 Generation of New Solutions......Page 212
4 Conclusions and Suggestions for Further Research......Page 213
References......Page 214
1 Introduction......Page 217
1.1 Problem of Stability of G......Page 219
1.2 Multidimensional Models......Page 220
2 The Model......Page 224
3 $sigma $-Model Representation......Page 227
4 Cosmological and Spherically Symmetric Solutions......Page 230
5 Spherically Symmetric and Black Hole Solutions......Page 235
5.1 Black Hole Solutions......Page 237
6 Post-Newtonian Approximation......Page 239
7 Conclusions......Page 241
Appendix 2: Solutions with Block-Orthogonal Set of Vectors......Page 242
References......Page 244
Open Issues......Page 251