Maximally Slicing a Black Hole

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 ($u\ge 0,u\le 0$) of the Kruskal diagram, tending asymptotically to the hypersurface $r=\frac{3}{2}M$ and avoiding the singularity at $r=0\mathrm{}$. Maximality is therefore a potentially useful condition to impose in obtaining computer solutions of Einstein's equations.