Tracking black holes in numerical relativity

Scott A. Caveny, Matthew Anderson, and Richard A. Matzner
Phys. Rev. D 68, 104009 – Published 11 November 2003
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Abstract

This work addresses the problem of generically tracking black hole event horizons in computational simulation of black hole interactions. Solutions of the hyperbolic eikonal equation, solved on a curved spacetime manifold containing black hole sources, are employed in development of a robust tracking method capable of continuously monitoring arbitrary changes of topology in the event horizon as well as arbitrary numbers of gravitational sources. The method makes use of continuous families of level set viscosity solutions of the eikonal equation with identification of the black hole event horizon obtained by the signature feature of discontinuity formation in the eikonal’s solution. The method is employed in the analysis of the event horizon for the asymmetric merger in a binary black hole system. In this first such three dimensional analysis, we establish both qualitative and quantitative evidence for our method and its application to the asymmetric problem. We focus attention on (1) the topology of the throat connecting the holes following merger, (2) the time of merger, and (3) continuing to account for the surface of section areas of the black hole sources.

  • Received 1 April 2003

DOI:https://doi.org/10.1103/PhysRevD.68.104009

©2003 American Physical Society

Authors & Affiliations

Scott A. Caveny, Matthew Anderson, and Richard A. Matzner

  • Center for Relativity, The University of Texas at Austin, Austin, Texas 78712-1081, USA

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Issue

Vol. 68, Iss. 10 — 15 November 2003

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