A Parallel Adaptive Event Horizon Finder for Numerical Relativity

TL;DR

This paper presents a new parallel adaptive algorithm and code for locating and exploring event horizons in numerical relativity simulations, enhancing accuracy and efficiency in studying black hole spacetimes.

Contribution

It introduces a novel parallel adaptive event horizon finder using Delaunay triangulation and efficient geodesic integration methods for numerical relativity.

Findings

Successfully locates complex event horizon features like toroidal holes

Achieves high accuracy in geodesic evolution equations

Demonstrates efficiency and adaptability in simulations

Abstract

With Advanced LIGO detecting the gravitational waves emitted from a pair of merging black holes in late 2015, we have a new perspective into the strong field regime of binary black hole systems. Event horizons are the defining features of such black hole spacetimes. We introduce a new code for locating event horizons in numerical simulations based on a Delaunay triangulation on a topological sphere. The code can automatically refine arbitrary regions of the event horizon surface to find and explore features such as the hole in a toroidal event horizon, as discussed in our companion paper. We also investigate various ways of integrating the geodesic equation and find evolution equations that can be integrated efficiently with high accuracy.