Numerical evolution of black holes with a hyperbolic formulation of general relativity

We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York. This is the first time this formulation has been used to evolve a numerical spacetime containing a black here. We excise the hale from the computational grid in order to avoid the central singularity. We describe in detail a causal differencing method that should allow one to stably evolve a hyperbolic system of equations in three spatial dimensions with an arbitrary shift vector. to second-order accuracy in both space and time. We demonstrate the success of this method in the spherically symmetric case. [S0556-2821(97)06072-0].