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Implementing an apparent-horizon finder in three dimensions

Thomas W. Baumgarte·Gregory B. Cook·Mark A. Scheel·Stuart L. Shapiro·Saul A. Teukolsky
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Abstract

Locating apparent horizons is not only important for a complete understanding of numerically generated spacetimes, but it may also be a crucial component of the technique for evolving black-hole spacetimes accurately. A scheme proposed by Libson et al., based on expanding the location of the apparent horizon in terms of symmetric trace-free tensors, seems very promising for use with three-dimensional numerical data sets. In this paper, we generalize this scheme and perform a number of code tests to fully calibrate its behavior in black-hole spacetimes similar to those we expect to encounter in solving the binary black-hole coalescence problem. An important aspect of the generalization is that we can compute the symmetric trace-free tensor expansion to any order. This enables us to determine how far we must carry the expansion to achieve results of a desired accuracy. To accomplish this generalization, we describe a new and very convenient set of recurrence relations which apply to symmetric trace-free tensors.

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Thomas W. Baumgarte, Gregory B. Cook, Mark A. Scheel, Stuart L. Shapiro, Saul A. Teukolsky. 1996-06-06. Implementing an apparent-horizon finder in three dimensions. https://doi.org/10.1103/physrevd.54.4849

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