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 spacelike 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 is as efficient as the currently fastest methods developed recently by Schnetter [Class. Quantum Grav. 20, 4719 (2003)] and Thornburg [Class. Quantum Grav. 21, 743 (2004)]. 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 ∼ 10 for the fractional error in the horizon’s location on a 2 GHz processor. PACS numbers: 04.25.Dm, 04.70.Bw, 02.70.Hm