Maximally Slicing a Black Hole

F. Estabrook, H. Wahlquist, S. Christensen, B. DeWitt, L. Smarr and E. Tsiang, Physical Review D7, 2814-2817, (1973).

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≥0,u≤0) of the Kruskal diagram, tending asymptotically to the hypersurface r=32M and avoiding the singularity at r=0. Maximality is therefore a potentially useful condition to impose in obtaining computer solutions of Einstein’s equations.