Maximal Hypersurfaces in Asymptotically Stationary Space-Times

TL;DR

This paper proves the existence of maximal hypersurfaces and their foliations in certain asymptotically flat spacetimes with symmetries, including cases with black holes, white holes, and ergoregions, advancing understanding of spacetime geometry.

Contribution

It establishes the existence of maximal hypersurfaces and foliations in two classes of asymptotically flat spacetimes with specific symmetry properties, including spacetimes with black and white holes.

Findings

Existence of maximal hypersurfaces in asymptotically flat spacetimes with timelike isometry groups.

Construction of foliations by maximal hypersurfaces in these spacetimes.

Extension of results to spacetimes containing black holes, white holes, and ergoregions.

Abstract

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 $S$.