Constant crunch coordinates for black hole simulations - art. no. 064024

We reinvestigate the utility of time-independent constant mean curvature fo liations for the numerical simulation of a single spherically symmetric bla ck hole. Each spacelike hypersurface of such a foliation is endowed with th e same constant value of the trace of the extrinsic curvature tensor K. Of the three families of K-constant surfaces possible (classified according to their asymptotic behaviors), we single out a subfamily of singularity avoi ding surfaces that may be particularly useful, and provide an analytic expr ession for the closest approach such surfaces make to the singularity. We t hen utilize a nonzero shift to yield families of K-constant surfaces which (1) avoid the black hole singularity, and thus the need to excise the singu larity, (2) are asymptotically null, aiding in gravity wave extraction, (3) cover the physically relevant part of the spacetime, (4) are well behaved (regular) across the horizon, and (5) are static under evolution, and there fore have no "grid stretching/sucking" pathologies. Preliminary numerical r uns demonstrate that we can stably evolve a single spherically symmetric st atic black hole using this foliation. We wish to emphasize that this coordi natization produces K-constant surfaces for a single black hole spacetime t hat are regular, static, and stable throughout their evolution.