Dependence of Self-force on Central Object

TL;DR

This paper investigates how the self-force on a particle orbiting a static spherically symmetric body varies with the interior structure of the central object, providing a practical method to compare different interior models.

Contribution

It derives a general mode-sum expression for the self-force difference due to interior metric changes, applicable to scalar, electromagnetic, and gravitational cases, simplifying computations.

Findings

Self-force is independent of central body type for static charges in minimally coupled scalar and electromagnetic cases.

For scalar charges in thin-shell spacetimes, the fractional change in self-force is larger for the radial component than for the angular component.

Radial self-force differences between black hole and thin-shell spacetimes are consistent for static charges and circular orbits at the same radius.

Abstract

For a particle in orbit about a static spherically symmetric body, we study the change in self-force that results when the central body type (i.e., the choice of interior metric for the Schwarzschild exterior) is changed. While a straight self-force is difficult to compute because of the need for regularization, such a "self-force difference" may be computed directly from the mode functions of the relevant wave equations. This technique gives a simple probe of the (non)locality of the force, as well as offers the practical benefit of an easy determination of the self-force on a body orbiting an arbitrary (static spherically symmetric) central body, once the corresponding result for a black hole (or some other reference interior) is known. We derive a general expression for the self-force difference at the level of a mode-sum in the case of a (possibly non-minimally coupled) scalar charge and indicate the generalization to the electromagnetic and gravitational cases. We then consider specific choices of orbit and/or central body. Our main findings are: (1) For charges held static at a large distance from the central body, the self-force is independent of the central body type in the minimally coupled scalar case and the electromagnetic case (but dependent in the nonminimally coupled scalar case); (2) For circular orbits about a thin-shell spacetime in the scalar case, the fractional change in self-force from a black hole spacetime is much larger for the radial (conservative) force than for the angular (dissipative) force; and (3) the radial self-force difference (between these spacetimes) agrees closely for a static charge and a circular orbit of the same radius.