Maximally slicing a black hole.

Abstract

Analytic and computer-derived solutions are presented of the problem of slicing the Schwarzschild geometry into asymptotically flat, asymptotically static, maximal spacelike hypersurfaces. The sequence of hypersurfaces advances forward in time in both halves (u greater than or equal to 0, u less than or equal to 0) of the Kruskal diagram, tending asymptotically to the hypersurface r = 3/2 M and avoiding the singularity at r = 0. Maximality is therefore a potentially useful condition to impose in obtaining computer solutions of Einstein's equations.