Adaptive computation of gravitational waves from black hole interactions

TL;DR

This paper introduces a new 3D PDE framework for simulating black hole perturbations, enabling efficient adaptive mesh refinement and providing the first fully resolved 3D solutions of such equations.

Contribution

It develops a unified PDE approach for all radiative modes of black hole perturbations in 3D, facilitating advanced numerical simulations with adaptive mesh refinement.

Findings

First fully resolved 3D solutions of black hole perturbation equations

Demonstrates computational savings with adaptive mesh refinement

Provides insights into simulating distorted black holes

Abstract

We construct a class of linear partial differential equations describing general perturbations of non-rotating black holes in 3D Cartesian coordinates. In contrast to the usual approach, a single equation treats all radiative $\ell -m$ modes simultaneously, allowing the study of wave perturbations of black holes with arbitrary 3D structure, as would be present when studying the full set of nonlinear Einstein equations describing a perturbed black hole. This class of equations forms an excellent testbed to explore the computational issues of simulating black spacetimes using a three dimensional adaptive mesh refinement code. Using this code, we present results from the first fully resolved 3D solution of the equations describing perturbed black holes. We discuss both fixed and adaptive mesh refinement, refinement criteria, and the computational savings provided by adaptive techniques in 3D for such model problems of distorted black holes.