Finding black holes in numerical spacetimes

Abstract

We have constructed a numerical code that finds black hole event horizons in an axisymmetric rotating spacetime. The spacetime is specified numerically by giving metric coefficients on a spatial grid for a series of time slices. The code solves the geodesic equation for light rays emitted from a suitable sample of points in the evolving spacetime. The algorithm for finding the event horizon employs the apparent horizon, which can form much later than the event horizon, to distinguish between light rays that escape to infinity and light rays that are captured. Simple geometries can be diagnosed on a workstation; more complicated cases are computationally intensive. However, the code is easily parallelized and has been efficiently run on the IBM SP-1 parallel machine. We have illustrated the use of the event horizon code on two cases. One is the head-on collision of two black holes that form from the collapse of collisionless matter, coalescing to a single Schwarzschild black hole. The other is the collapse of a rotating toroid to form a Kerr black hole. In this case the horizon initially appears with a toroidal topology. This is the first known example of this phenomenon.

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