Apparent horizons for boosted or spinning black holes.

Abstract

As part of an ongoing study of initial data for black-hole collisions, we examine the apparent horizons in initial-data sets for a single black hole with either translational or rotational velocity constructed using a systematic and easily generalized formalism. The apparent-horizon equation is formulated as a boundary-value problem that, with small changes, will be applicable to nonaxisymmetric problems. We find all apparent horizons in our numerically generated sets of initial data. A previously known exact result for spinning holes is reproduced numerically. We find new results, both exact and numerical, for the apparent horizons of black holes with linear momentum. In some of these cases an interesting structure emerges in which the apparent horizons and minimal surface intersect one another.