Generic effective sources for first-order in mass-ratio gravitational self-force calculations in Schwarzschild spacetime

TL;DR

This paper introduces an analytic framework for constructing effective sources to compute the gravitational self-force for generic orbits in Schwarzschild spacetime, improving numerical efficiency and regularization.

Contribution

It presents the first fully analytic method for creating effective sources using angular modulation and scalar modes for self-force calculations in Schwarzschild spacetime.

Findings

Effective source constructed with scalar modes is continuous across the worldline.

Framework enables efficient 1+1 dimensional numerical implementation.

Replaces traditional regularization with an analytic reformulation.

Abstract

The numerical calculation of gravitational self-force in extreme mass ratio inspiral systems is fundamentally challenging due to the singular nature of point-particle sources. To overcome these difficulties, the effective source method offers an innovative alternative by replacing traditional regularization techniques with a reformulation of the problem. In this paper, we present the first fully analytic framework for constructing effective sources to compute the gravitational self-force for generic orbits in Schwarzschild spacetime. By reformulating the singular field through angular modulation in terms of a tetrad decomposition, the effective source can be constructed with the linear combination of scalar modes. The derived effective source is continuous across the particle's worldline, enabling efficient numerical implementation in $1+1$ dimensions.