Self-force on an arbitrarily coupled static scalar particle in a wormhole space-time

TL;DR

This paper derives an explicit analytic expression for the self-force on a static scalar charge in a wormhole space-time with arbitrary coupling to curvature, revealing how the force varies with coupling and identifying divergence points.

Contribution

It provides a closed-form Green's function and self-force expression for arbitrary coupling, extending previous numerical and special-case analytic results in wormhole space-times.

Findings

Self-force depends on the coupling to curvature.

Force changes sign at the conformal coupling value.

Self-force diverges at specific coupling constants.

Abstract

In this paper, we consider the problem of computing the self-force and self-energy for a static scalar charge in a wormhole space-time with throat profile $r(\rho)=\sqrt{\rho^{2}+a^{2}}$ for arbitrary coupling of the field to the curvature. This calculation has previously been considered numerically by Bezerra and Khusnutdinov, while analytic results have been obtained in the special cases of minimal ($\xi=0$) coupling and conformal coupling ($\xi=1/8$ in three dimensions). We present here a closed form expression for the static Green's function for arbitrary coupling and hence we obtain an analytic expression for the self-force. The self-force depends crucially on the coupling of the field to the curvature of the space-time and hence it is useful to determine the dependence explicitly. The numerical computation can identify some qualitative aspects of this dependence such as the change in the sign of the force as it passes through the conformally coupled value, as well as the fact that the self-force diverges for $\xi=1/2$. From the closed form expression, it is straight-forward to see that there is an infinite set of values of the coupling constant for which the self-force diverges, but we also see that there is an infinite set of values for which the self-force vanishes.