Effective source approach to self-force calculations

TL;DR

This paper reviews the effective source method for self-force calculations, introduces new techniques for generic orbits and boundary conditions, and discusses future challenges in the field.

Contribution

It presents a comprehensive review of the effective source approach, introduces a new effective source for generic orbits, and implements hyperboloidal slicing to improve boundary condition handling.

Findings

Successful construction of an effective source for generic orbits

Implementation of hyperboloidal slicing improves boundary conditions

Identifies key issues for future development

Abstract

Numerical evaluation of the self-force on a point particle is made difficult by the use of delta functions as sources. Recent methods for self-force calculations avoid delta functions altogether, using instead a finite and extended "effective source" for a point particle. We provide a review of the general principles underlying this strategy, using the specific example of a scalar point charge moving in a black hole spacetime. We also report on two new developments: (i) the construction and evaluation of an effective source for a scalar charge moving along a generic orbit of an arbitrary spacetime, and (ii) the successful implementation of hyperboloidal slicing that significantly improves on previous treatments of boundary conditions used for effective-source-based self-force calculations. Finally, we identify some of the key issues related to the effective source approach that will need to be addressed by future work.