Gb. Cook et Ma. Scheel, WELL-BEHAVED HARMONIC TIME SLICES OF A CHARGED, ROTATING, BOOSTED BLACK-HOLE, Physical review. D. Particles and fields, 56(8), 1997, pp. 4775-4781
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.