Self force via $m$-mode regularization and 2+1D evolution: II. Scalar-field implementation on Kerr spacetime

TL;DR

This paper presents a novel time-domain method for calculating the scalar-field self-force in Kerr spacetime, utilizing m-mode regularization and 2+1D evolution, successfully applied to circular orbits around a Kerr black hole.

Contribution

It introduces a practical, adaptable time-domain approach for self-force computations in Kerr spacetime using m-mode regularization and numerical evolution.

Findings

First time-domain scalar self-force calculation in Kerr geometry

Code reproduces frequency-domain results accurately

Method is adaptable for gravitational self-force computations

Abstract

This is the second in a series of papers aimed at developing a practical time-domain method for self-force calculations in Kerr spacetime. The key elements of the method are (i) removal of a singular part of the perturbation field with a suitable analytic "puncture" based on the Detweiler--Whiting decomposition, (ii) decomposition of the perturbation equations in azimuthal ($m$-)modes, taking advantage of the axial symmetry of the Kerr background, (iii) numerical evolution of the individual $m$-modes in 2+1-dimensions with a finite difference scheme, and (iv) reconstruction of the physical self-force from the mode sum. Here we report an implementation of the method to compute the scalar-field self-force along circular equatorial geodesic orbits around a Kerr black hole. This constitutes a first time-domain computation of the self force in Kerr geometry. Our time-domain code reproduces the results of a recent frequency-domain calculation by Warburton and Barack, but has the added advantage of being readily adaptable to include the back-reaction from the self force in a self-consistent manner. In a forthcoming paper---the third in the series---we apply our method to the gravitational self-force (in the Lorenz gauge).