Discontinuous Galerkin method for computing gravitational waveforms from extreme mass ratio binaries

TL;DR

This paper presents a discontinuous Galerkin numerical method for accurately computing gravitational waveforms from extreme mass ratio binaries, effectively handling discontinuities in the wave equations.

Contribution

The paper introduces a novel dG method for 1+1 wave equations in EMRBs, achieving spectral accuracy despite discontinuities, and discusses potential extensions to include self-force effects.

Findings

Achieves global spectral accuracy in waveform computation

Handles jump discontinuities effectively in the wave equations

Demonstrates promising numerical results for EMRB modeling

Abstract

Gravitational wave emission from extreme mass ratio binaries (EMRBs) should be detectable by the joint NASA-ESA LISA project, spurring interest in analytical and numerical methods for investigating EMRBs. We describe a discontinuous Galerkin (dG) method for solving the distributionally forced 1+1 wave equations which arise when modeling EMRBs via the perturbation theory of Schwarzschild blackholes. Despite the presence of jump discontinuities in the relevant polar and axial gravitational "master functions", our dG method achieves global spectral accuracy, provided that we know the instantaneous position, velocity, and acceleration of the small particle. Here these variables are known, since we assume that the particle follows a timelike geodesic of the Schwarzschild geometry. We document the results of several numerical experiments testing our method, and in our concluding section discuss the possible inclusion of gravitational self-force effects.