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

Understand

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.