Numerical Radiation Reaction for a Scalar Charge in Kerr Circular Orbit

TL;DR

This paper numerically computes the dissipative self-force on a scalar charge in a Kerr spacetime orbit, comparing direct and flux-based methods, and confirms their agreement through numerical and analytical analysis.

Contribution

It introduces a numerical approach to calculate the scalar self-force in Kerr spacetime and verifies the consistency of direct and flux-based methods.

Findings

Force per mode matches for both methods

Numerical solutions are matched to asymptotic expansions

Recursion relations for asymptotic coefficients are provided

Abstract

We numerically calculate the dissipative part of the self-force on a scalar charge moving on a circular, geodesic, equatorial orbit in Kerr spacetime. The solution to the scalar field equation is computed by separating variables and is expressed as a mode sum over radial and angular modes. The force is then computed in two ways: a direct, instantaneous force calculation which uses the half-retarded-minus-half-advanced field, and an indirect method which uses the energy and angular momentum flux at the horizon and at infinity to infer the force. We are able to show numerically and analytically that the force-per-mode is the same for both methods. To enforce the boundary conditions (ingoing radiation at the horizon and outgoing radiation at infinity for the retarded solution) numerical solutions to the radial equation are matched to asymptotic expansions for the fields at the boundaries. Recursion relations for the coefficients in the asymptotic expansions are given in an appendix.