Spectral-infinite element method approach for computing asymptotically flat initial data sets in general relativity

TL;DR

This paper presents a spectral-infinite element numerical method for solving Einstein's constraint equations, enabling the computation of asymptotically flat perturbations of Kerr black holes with high accuracy.

Contribution

It introduces a novel spectral-infinite element approach combining spin-weighted spherical harmonics and infinite elements for Einstein's equations in unbounded domains.

Findings

Successfully computes asymptotically flat perturbations of Kerr black holes.

Demonstrates high accuracy in solving Einstein's constraint equations.

Provides a new computational tool for general relativity simulations.

Abstract

In this work, we introduce a spectral-infinite element method for solving Einstein's constraint equations in hyperbolic form. As an application of this, we use this method for computing asymptotically flat perturbations of a Kerr black hole with small angular momentum. Our numerical infrastructure is based on the use of a spin-weighted spherical harmonic transform combined with an infinite element method for solving partial differential equations in unbounded domains.