Pseudospectral apparent horizon finders: An efficient new algorithm

We review the problem of finding an apparent horizon in Cauchy data $\left(\Sigma {,g}_{\mathrm{ab}}{,K}_{\mathrm{ab}}\right)$ in three space dimensions without symmetries. We describe a family of algorithms which includes the pseudospectral 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.