Regularization parameters for the self force in Schwarzschild spacetime: II. gravitational and electromagnetic cases

TL;DR

This paper derives all necessary regularization parameters for calculating gravitational and electromagnetic self forces on particles in Schwarzschild spacetime, enabling practical mode-sum computations for arbitrary geodesic orbits.

Contribution

It provides the complete set of regularization parameters for gravitational and electromagnetic self forces, including the first derivation for electromagnetic cases, facilitating accurate self-force calculations.

Findings

Derived all regularization parameters for gravitational self force.

Obtained electromagnetic regularization parameters for the first time.

Enabled practical mode-sum calculations for self forces in Schwarzschild spacetime.

Abstract

We obtain all ``regularization parameters'' (RP) needed for calculating the gravitational and electromagnetic self forces for an arbitrary geodesic orbit around a Schwarzschild black hole. These RP values are required for implementing the previously introduced mode-sum method, which allows a practical calculation of the self force by summing over contributions from individual multipole modes of the particle's field. In the gravitational case, we provide here full details of the analytic method and results briefly reported in a recent Letter [Phys. Rev. Lett. {\bf 88}, 091101 (2002)]. In the electromagnetic case, the RP are obtained here for the first time.