Scalar self-force for eccentric orbits around a Schwarzschild black hole

TL;DR

This paper develops a method to compute the scalar self-force on particles in eccentric orbits around a Schwarzschild black hole, extending previous circular orbit calculations and introducing novel visualization techniques.

Contribution

It extends scalar self-force calculations from circular to eccentric orbits using a regularized source and 3D evolution, with innovative visualization of self-force loops.

Findings

Good agreement with previous (1+1) code results

Successful extension to eccentric orbits

Introduction of self-force loop visualizations

Abstract

We revisit the problem of computing the self-force on a scalar charge moving along an eccentric geodesic orbit around a Schwarzschild black hole. This work extends previous scalar self-force calculations for circular orbits, which were based on a regular "effective" point-particle source and a full 3D evolution code. We find good agreement between our results and previous calculations based on a (1+1) time-domain code. Finally, our data visualization is unconventional: we plot the self-force through full radial cycles to create "self-force loops", which reveal many interesting features that are less apparent in standard presentations of eccentric-orbit self-force data.