Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application

TL;DR

This paper introduces a novel regularization method for self-force calculations in curved spacetime by directly regularizing the retarded field, simplifying computations and avoiding singular source modeling, demonstrated through a scalar charge in Schwarzschild spacetime.

Contribution

The paper presents a new approach that regularizes the retarded field itself, enabling easier and more accurate self-force calculations in curved spacetime.

Findings

Achieved agreement with frequency-domain results to ~0.1%.

Successfully implemented a 4th-order time-domain code for a scalar charge.

Demonstrated the method's effectiveness in a Schwarzschild black hole scenario.

Abstract

We propose an approach for the calculation of self-forces, energy fluxes and waveforms arising from moving point charges in curved spacetimes. As opposed to mode-sum schemes that regularize the self-force derived from the singular retarded field, this approach regularizes the retarded field itself. The singular part of the retarded field is first analytically identified and removed, yielding a finite, differentiable remainder from which the self-force is easily calculated. This regular remainder solves a wave equation which enjoys the benefit of having a non-singular source. Solving this wave equation for the remainder completely avoids the calculation of the singular retarded field along with the attendant difficulties associated with numerically modeling a delta function source. From this differentiable remainder one may compute the self-force, the energy flux, and also a waveform which reflects the effects of the self-force. As a test of principle, we implement this method using a 4th-order (1+1) code, and calculate the self-force for the simple case of a scalar charge moving in a circular orbit around a Schwarzschild black hole. We achieve agreement with frequency-domain results to ~ 0.1% or better.