WELL-BEHAVED HARMONIC TIME SLICES OF A CHARGED, ROTATING, BOOSTED BLACK-HOLE

Harmonic time slicings are used in some hyperbolic formulations of Ein stein's equations and are therefore of considerable interest to the fi eld of numerical relativity. We construct an analytic coordinate repre sentation of the Kerr-Newman geometry that is harmonic in both its spa tial and temporal coordinates. The metric is independent of time and t he spacelike, t= const slices extend from spatial infinity smoothly th rough the event horizon at r=r(+) and end at the Cauchy horizon at r=r (_). When the spatial harmonic coordinate condition is imposed, there is also a spatial coordinate singularity at r=M, but this fully harmon ic metric can be trivially boosted to yield an analytic solution for a harmonically sliced translating, spinning black hole. We also examine the behavior of evolutions which obey the harmonic slicing condition but start from initial data that is not in the time-independent harmon ic slicing foliation. We find that with a suitable choice of the spati al gauge, the evolving three-geometry is ''attracted'' to the time-ind ependent three-geometry we present in this paper. [S0556-2821(97)02020 -1]. PACS number(s): 04.25.Dm, 04.20.Jb, 04.70.Bw.