Generic effective sources for first-order in mass-ratio gravitational self-force calculations in Schwarzschild spacetime
arXiv:2505.19732 · doi:10.1103/z9jr-qxc7
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 dimensions.
29 pages, 6 figures; comments are welcome, match the published version in PRD
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