New Coordinate Systems for Axisymmetric Black Hole Collisions

TL;DR

This paper introduces a new method for generating orthogonal coordinate systems to improve numerical simulations of axisymmetric black hole collisions, offering enhanced stability and extendibility.

Contribution

The authors develop a novel grid generation procedure for orthogonal coordinates, facilitating more stable and extendible simulations of black hole mergers.

Findings

Good agreement with previous results in waveform profiles

Comparable total radiated energies to established calculations

Coordinates are more easily extendible to complex black hole scenarios

Abstract

We describe a grid generation procedure designed to construct new classes of orthogonal coordinate systems for binary black hole spacetimes. The computed coordinates offer an alternative approach to current methods, in addition to providing a framework for potentially more stable and accurate evolutions of colliding black holes. As a particular example, we apply our procedure to generate appropriate numerical grids to evolve Misner's axisymmetric initial data set representing two equal mass black holes colliding head-on. These new results are compared with previously published calculations, and we find generally good agreement in both the waveform profiles and total radiated energies over the allowable range of separation parameters. Furthermore, because no specialized treatment of the coordinate singularities is required, these new grids are more easily extendible to unequal mass and spinning black hole collisions.