A new spectral apparent horizon finder for 3D numerical relativity

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 ( l = 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 as efficient as the currently fastest methods recently developed by Schnetter ( 2003 Class. Quantum Grav. 20 4719) and Thornburg ( 2004 Class. Quantum Grav. 21 743). At typical resolutions it takes only 0.5 s to find the apparent horizon of a Kerr-Schild black hole with a = 0.9M to the accuracy - 10(-5) for the fractional error in the horizon's location on a 2 GHz processor.