General Relativity and the Einstein EquationsOUP Oxford, 4 gru 2008 - 816 General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field. |
Spis treści
| 1 | |
| 19 | |
| 37 | |
Schwarzschild spacetime and black holes | 72 |
Cosmology | 106 |
Local Cauchy problem | 142 |
Constraints | 179 |
Other hyperbolicelliptic wellposed systems | 238 |
Global hyperbolicity and causality | 371 |
Singularities | 402 |
Stationary spacetimes and black holes | 451 |
Global existence theorems asymptotically Euclidean data | 482 |
Global existence theorems the cosmological case | 510 |
APPENDICES | 534 |
RELATED PAPERS | 663 |
| 771 | |
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