ON MAXIMAL SURFACES IN ASYMPTOTICALLY FLAT SPACE-TIMES

Existenc of maximal and "almost maximal" hypersurfaces in asymptotically flat space-times is established under boundary conditions weaker than those considered previously. We show in particular that every vacuum evolution of asymptotically flat data for the Einstein equations can be foliated by slices maximal outside a spatially compact set and that every (strictly) stationary asymptotically flat space-time can be foliated by maximal hypersurfaces. Amongst other uniqueness results, we show that maximal hypersurfaces can be used to "partially fix" an asymptotic Poincaré group. © 1990 Springer-Verlag.