Simple, efficient method of calculating the Detweiler-Whiting singular field to very high order

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 four-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 orders in perturbation theory.

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