Simple, efficient method of calculating the Detweiler-Whiting singular field to very high order
arxiv(2024)
Abstract
Most self-force calculations rely, in one way or another, on representations
of a particle's Detweiler- Whiting singular field. We present a simple method
of calculating the singular field to high order in a local expansion in powers
of distance from the particle. As a demonstration, we compute the singular
field to 14th order in distance, 10 orders beyond the previous state of the
art, in the simple case of a scalar charge in circular orbit around a
Schwarzschild black hole. We provide the result in both a 4-dimensional form
and a decomposed form suitable for use in an m-mode puncture scheme. Our method
should have applications in overcoming bottlenecks in current self-force
calculations at both first and second order in perturbation theory.
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