Three dimensional distorted black holes: using the Galerkin-Collocation method

TL;DR

This paper introduces a Galerkin-Collocation numerical method to generate accurate initial data for three-dimensional distorted black holes, analyzing their mass and gravitational wave distribution.

Contribution

The paper develops a novel combination of Galerkin and Collocation methods for initial data construction in 3D black hole simulations, enhancing accuracy.

Findings

Accurate initial data for distorted black holes obtained.

Computed ADM mass of initial data sets.

Analyzed gravitational wave angular distribution.

Abstract

We present an implementation of the Galerkin-Collocation method to determine the initial data for non-rotating distorted three dimensional black holes in the inversion and puncture schemes. The numerical method combines the key features of the Galerkin and Collocation methods which produces accurate initial data. We evaluated the ADM mass of the initial data sets, and we have provided the angular structure of the gravitational wave distribution at the initial hypersurface by evaluating the scalar $\Psi_4$ for asymptotic observers.