A Finite Element Computation of the Gravitational Radiation emitted by a Point-like object orbiting a Non-rotating Black Hole

TL;DR

This paper introduces a finite element computational method in the time domain to accurately model gravitational perturbations caused by a small orbiting object around a non-rotating black hole, relevant for gravitational wave detection.

Contribution

The paper presents a novel finite element approach for solving perturbation equations of black holes due to orbiting objects, improving accuracy in modeling extreme-mass-ratio binaries.

Findings

Method achieves high accuracy compared to previous results

Finite element approach effectively models wave-type perturbations

Potential for improved gravitational wave signal predictions

Abstract

The description of extreme-mass-ratio binary systems in the inspiral phase is a challenging problem in gravitational wave physics with significant relevance for the space interferometer LISA. The main difficulty lies in the evaluation of the effects of the small body's gravitational field on itself. To that end, an accurate computation of the perturbations produced by the small body with respect the background geometry of the large object, a massive black hole, is required. In this paper we present a new computational approach based on Finite Element Methods to solve the master equations describing perturbations of non-rotating black holes due to an orbiting point-like object. The numerical computations are carried out in the time domain by using evolution algorithms for wave-type equations. We show the accuracy of the method by comparing our calculations with previous results in the literature. Finally, we discuss the relevance of this method for achieving accurate descriptions of extreme-mass-ratio binaries.