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.... asymptotically Euclidean a spacetime (V, g) where V = M A R, the sections (Mt, t) are asymptotically Euclidean, and on each Mt the lapse tends to 1 and the shift tends to zero at infinity. ... 28 Klainerman, S. andNicolo, F. (2002) The Evolution Problem in General Relativity, Birkhauser. ... Similar inequalities on asymptotically Euclidean manifolds are stated in Appendix I. 35 Loizelet, J. (2005 ) C. R. Acad.

Title | : | General Relativity and the Einstein Equations |

Author | : | Yvonne Choquet-Bruhat |

Publisher | : | OUP Oxford - 2008-12-04 |

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