Generic effective source for scalar self-force calculations

TL;DR

This paper introduces a universal method for calculating an effective source for scalar self-force problems, enabling finite and continuous solutions applicable to various geodesic motions in black hole spacetimes.

Contribution

It presents a new, general approach for computing an effective source that is finite and continuous, applicable to arbitrary geodesic motion in any background spacetime.

Findings

Method successfully applied to circular orbits in Schwarzschild and Kerr spacetimes.

Provides numerical C code for effective source computation in different orbital configurations.

Demonstrates the approach's applicability to highly spinning Kerr black holes.

Abstract

A leading approach to the modelling of extreme mass ratio inspirals involves the treatment of the smaller mass as a point particle and the computation of a regularized self-force acting on that particle. In turn, this computation requires knowledge of the regularized retarded field generated by the particle. A direct calculation of this regularized field may be achieved by replacing the point particle with an effective source and solving directly a wave equation for the regularized field. This has the advantage that all quantities are finite and require no further regularization. In this work, we present a method for computing an effective source which is finite and continuous everywhere, and which is valid for a scalar point particle in arbitrary geodesic motion in an arbitrary background spacetime. We explain in detail various technical and practical considerations that underlie its use in several numerical self-force calculations. We consider as examples the cases of a particle in a circular orbit about Schwarzschild and Kerr black holes, and also the case of a particle following a generic time-like geodesic about a highly spinning Kerr black hole. We provide numerical C code for computing an effective source for various orbital configurations about Schwarzschild and Kerr black holes.