Event Horizons in Numerical Relativity I: Methods and Tests

TL;DR

This paper introduces and tests new numerical methods for accurately locating event horizons in simulated black hole spacetimes, including complex and dynamic scenarios.

Contribution

It presents a novel approach combining backward integration and horizon surface integration to locate event horizons in numerical relativity.

Findings

Methods achieve high accuracy within a small fraction of a grid zone.

Applicable to various black hole configurations, including distorted and colliding black holes.

Validated on both analytic and numerical spacetimes.

Abstract

This is the first paper in a series on event horizons in numerical relativity. In this paper we present methods for obtaining the location of an event horizon in a numerically generated spacetime. The location of an event horizon is determined based on two key ideas: (1) integrating backward in time, and (2) integrating the whole horizon surface. The accuracy and efficiency of the methods are examined with various sample spacetimes, including both analytic (Schwarzschild and Kerr) and numerically generated black holes. The numerically evolved spacetimes contain highly distorted black holes, rotating black holes, and colliding black holes. In all cases studied, our methods can find event horizons to within a very small fraction of a grid zone.