Distorted Black Hole Initial Data Using the Puncture Method

TL;DR

This paper develops a method to generate initial data for distorted black holes using the puncture approach, employing elliptic equations and adaptive mesh refinement for accurate numerical simulations.

Contribution

It introduces a novel application of the puncture method to create both isometric and non-isometric distorted black hole initial data with improved numerical techniques.

Findings

Successfully generates distorted black hole initial data

Demonstrates the effectiveness of adaptive mesh refinement

Provides data comparable to previous isometry boundary condition methods

Abstract

We solve for single distorted black hole initial data using the puncture method, where the Hamiltonian constraint is written as an elliptic equation in R^3 for the nonsingular part of the metric conformal factor. With this approach we can generate isometric and non--isometric black hole data. For the isometric case, our data are directly comparable to those obtained by Bernstein et al., who impose isometry boundary conditions at the black hole throat. Our numerical simulations are performed using a parallel multigrid elliptic equation solver with adaptive mesh refinement. Mesh refinement allows us to use high resolution around the black hole while keeping the grid boundaries far away in the asymptotic region.