Pseudo-spectral apparent horizon finders: an efficient new algorithm

TL;DR

This paper introduces a new pseudo-spectral algorithm for efficiently and robustly finding apparent horizons in three-dimensional numerical relativity data, improving speed and reliability over previous methods.

Contribution

It presents a unified family of algorithms including existing methods and proposes a new, faster, and more robust algorithm for apparent horizon finding in 3D data.

Findings

New algorithm is faster than previous methods.

Algorithm demonstrates increased robustness in tests.

Effective on Brill-Lindquist and Kerr initial data.

Abstract

We review the problem of finding an apparent horizon in Cauchy data (Sigma, g_ab, K_ab) in three space dimensions without symmetries. We describe a family of algorithms which includes the pseudo-spectral apparent horizon finder of Nakamura et al. and the curvature flow method proposed by Tod as special cases. We suggest that other algorithms in the family may combine the speed of the former with the robustness of the latter. A numerical implementation for Cauchy data given on a grid in Cartesian coordinates is described, and tested on Brill-Lindquist and Kerr initial data. The new algorithm appears faster and more robust than previous ones.