IMPLEMENTING AN APPARENT-HORIZON FINDER IN 3 DIMENSIONS

Locating apparent horizons is not only important for a complete unders tanding of numerically generated spacetimes, but it may also be a cruc ial component of the technique for evolving black-hole spacetimes accu rately. A scheme proposed by Libson, Masso, Seidel, and Suen, based on expanding the location of the apparent horizon in terms of symmetric trace-free tensors, seems very promising for use with three-dimensiona l numerical data sets. In this paper, we generalize this scheme and pe rform a number of code tests to fully calibrate its behavior in black- hole spacetimes similar to those we expect to encounter in solving the binary black-hole coalescence problem. An important aspect of the gen eralization is that we can compute the symmetric trace-free tensor exp ansion to any order. This enables us to determine how far we must carr y the expansion to achieve results of a desired accuracy. To accomplis h this generalization, we describe a new and very convenient set of re currence relations which apply to symmetric trace-free tensors.