High-order expansions of the Detweiler-Whiting singular field in Kerr spacetime

TL;DR

This paper extends high-order expansions of the Detweiler-Whiting singular field to Kerr spacetime, enabling improved self-force calculations for particles in equatorial orbits.

Contribution

It introduces new high-order expansions of the singular field in Kerr spacetime and derives previously unknown mode-sum regularization parameters.

Findings

Computed new mode-sum regularization parameters.

Extended singular field expansions to Kerr spacetime.

Proposed applications for m-mode regularization in self-force calculations.

Abstract

In a previous paper, we computed expressions for the Detweiler-Whiting singular field of point scalar, electromagnetic and gravitational charges following a geodesic of the Schwarzschild spacetime. We now extend this to the case of equatorial orbits in Kerr spacetime, using coordinate and covariant approaches to compute expansions of the singular field in scalar, electromagnetic and gravitational cases. As an application, we give the calculation of previously unknown mode-sum regularization parameters. We also propose a new application of high-order approximations to the singular field, showing how they may be used to compute $m$-mode regularization parameters for use in the $m$-mode effective source approach to self-force calculations.