Initial Data and Coordinates for Multiple Black Hole Systems

TL;DR

This paper introduces a novel method for setting initial data in simulations of multiple moving black hole systems, extending the Kerr-Schild form to improve computational modeling and horizon tracking.

Contribution

It generalizes the Kerr-Schild approach to multiple black holes, aiding in more accurate and efficient numerical simulations of such systems.

Findings

Preserves Kerr-Schild form near black holes

Simplifies horizon tracking in simulations

Provides coordinate choices for stable evolution

Abstract

We present here an alternative approach to data setting for spacetimes with multiple moving black holes generalizing the Kerr-Schild form for rotating or non-rotating single black holes to multiple moving holes. Because this scheme preserves the Kerr-Schild form near the holes, it selects out the behaviour of null rays near the holes, may simplify horizon tracking, and may prove useful in computational applications. For computational evolution, a discussion of coordinates (lapse function and shift vector) is given which preserves some of the properties of the single-hole Kerr-Schild form.