A double-domain spectral method for black hole excision data

TL;DR

This paper introduces a novel double-domain spectral method for accurately computing binary black hole initial data, effectively handling boundary conditions at horizons and applicable to extreme parameter cases.

Contribution

The paper presents a new spectral method that efficiently solves elliptic PDEs for binary black hole initial data with high accuracy and robustness in challenging scenarios.

Findings

Achieved highly accurate solutions with moderate computational effort.

Successfully handled limiting cases like large radius ratios.

Demonstrated applicability to quasi-stationary black hole configurations.

Abstract

In this paper a new double-domain spectral method to compute binary black hole excision initial data is presented. The method solves a system of elliptic partial differential equations in the exterior of two excised spheres. At the surface of these spheres, boundary conditions need to be imposed. As such, the method can be used to construct arbitrary initial data corresponding to binary black holes with specific boundary conditions at their apparent horizons. We give representative examples corresponding to initial data that fulfill the requirements of the quasi-stationary framework, which combines the thin sandwich formulation of the constraint equations with the isolated horizon conditions for black holes in quasi-equilibrium. For all examples considered, numerical solutions with extremely high accuracy were obtained with moderate computational effort. Moreover, the method proves to be applicable even when tending toward limiting cases such as large radius ratios for the black holes.