Geometric horizon for distorted black holes

Abstract

We previously proposed an equation for locating the geometric horizon of perturbed static spherically symmetric spacetimes using the Kretschmann scalar. The result was fully covariant, but not practical for dealing with perturbations. Here, we reformulate this geometric horizon detector into a more practical form, in terms of the spherical-harmonic coefficients of the metric perturbation that are the usual result of a perturbative calculation about spherically symmetric spacetimes. We apply our result to the Vaidya spacetime to demonstrate how the geometric horizon might differ from the traditional horizons found in the literature.