Maximal Hypersurfaces in Asymptotically Stationary Spacetimes

Existence of maximal hypersurfaces and of foliations by maximal hypersurfaces is proven in two classes of asymptotically flat spacetimes which possess a one parameter group of isometries whose orbits are timelike “near infinity”. The first class consists of strongly causal asymptotically flat spacetimes which contain no “black hole or white hole” (but may contain “ergoregions” where the Killing orbits fail to be timelike). The second class of spacetimes possess a black hole and a white hole, with the black and white hole horizons intersecting in a compact 2-surface S. Alexander von Humboldt fellow. On leave of absence from the Institute of Mathematics, Polish Academy of Sciences, Warsaw. E–mail: [email protected]. Supported in part by KBN grant #2 1047 9101. Supported in part by NSF grant PHY–8918388. E–mail: [email protected].