Waveform propagation in black hole spacetimes: evaluating the quality of numerical solutions

TL;DR

This paper evaluates the accuracy of three-dimensional numerical simulations of gravitational wave propagation and scattering in black hole spacetimes, using a generalized Zerilli equation as a testbed.

Contribution

It introduces a numerical approach for solving the generalized Zerilli equation in 3D Cartesian coordinates to study gravitational waves around black holes.

Findings

The numerical code accurately models wave propagation and scattering.

The approach effectively tests 3D gravitational wave computations near black holes.

Results validate the method's potential for complex spacetime simulations.

Abstract

We compute the propagation and scattering of linear gravitational waves off a Schwarzschild black hole using a numerical code which solves a generalization of the Zerilli equation to a three dimensional cartesian coordinate system. Since the solution to this problem is well understood it represents a very good testbed for evaluating our ability to perform three dimensional computations of gravitational waves in spacetimes in which a black hole event horizon is present.