Maximal hypersurfaces and positivity of mass

Choquet-bruhat, Y., A. E. Fischer and J. E. Marsden

In Isolated Gravitating Systems in General Relativity, Italian Physical Society, (J. Ehlers, ed.), (1979), 396-456


This paper discusses some recent results on the related problems of positivity of mass and the existence of maximal spacelike hypersurfaces $ \Sigma$ for asymptotically flat space-times. If k$\scriptstyle \Sigma$ denotes the second fundamental form of $ \Sigma$ , then $ \Sigma$ is called maximal if trk$\scriptstyle \Sigma$ = 0 , has constant mean extrinsic curvature if trk$\scriptstyle \Sigma$ = const on $ \Sigma$ , and is a moment of time-symmetry if k$\scriptstyle \Sigma$ = 0 .
We will give a certain amount of background material in order to keep the exposition self-contained. However, we so assume familiarity with the ADM formalism.