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A new spectral apparent horizon finder for 3D numerical relativity

Lap-Ming Lin·Jerome Novak
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Abstract

We present a new spectral-method-based algorithm for finding apparent horizons in three-dimensional space-like hypersurfaces without symmetries. While there are already a wide variety of algorithms for finding apparent horizons, our new algorithm does not suffer from the same weakness as previous spectral apparent horizon finders: namely the monopolar coefficient ($\ell=0$ in terms of the spherical harmonics decomposition) needed to be determined by a root-finding procedure. Hence, this leads to a much faster and more robust spectral apparent horizon finder. The finder is tested with the Kerr-Schild and Brill-Lindquist data. Our finder is accurate and is as efficient as the currently fastest methods developed recently by Schnetter (2003 Class. Quantum Grav. {\bf 20}, 4719) and Thornburg (2004 Class. Quantum Grav. {\bf 21}, 743). At typical resolutions it takes only 0.5 second to find the apparent horizon of a Kerr-Schild black hole with $a=0.9M$ to the accuracy $\sim 10^{-5}$ for the fractional error in the horizon's location on a 2 GHz processor.

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Lap-Ming Lin, Jerome Novak. 2007-05-02. A new spectral apparent horizon finder for 3D numerical relativity. https://doi.org/10.1088/0264-9381%2F24%2F10%2F012

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