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Published April 15, 1994 | Published
Journal Article Open

Finding black holes in numerical spacetimes


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.

Additional Information

© 1994 American Physical Society. (Received 5 November 1993) We thank Michael Blanton and Michael Chia for assistance with visualization and for help developing the horizon finder algorithm. We also thank Andrew Abrahams for useful discussions and Michael Piper for programming assistance in the early stages of the project. S.H., C.K, P.W., and K.W. were supported in part by the Research Experiences for Undergraduates program of the National Science Foundation. This research was supported in part by NSF Grants Nos. AST 91-19475 and PHY 90-07834 and NASA grant NAGW-2364 at Cornell University. Computations were performed at the Cornell Center for Theory and Simulation in Science and Engineering, which is supported in part by the National Science Foundation, IBM Corporation, New York State, and the Cornell Research Institute.

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Published - PhysRevD.49.4004.pdf


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August 20, 2023
August 20, 2023