Self-force on a scalar point charge in the long throat

TL;DR

This paper introduces an analytic WKB-based method to compute the self-force on a static scalar charge in an ultrastatic spacetime region called the long throat, considering a massless scalar field with specific curvature coupling.

Contribution

The paper develops a new analytic approach using WKB approximation to evaluate the self-force in a long throat spacetime for a scalar field with particular curvature coupling.

Findings

Provides explicit self-force calculations in the long throat region.

Demonstrates the applicability of WKB approximation in this context.

Offers insights into scalar field behavior in ultrastatic spacetimes.

Abstract

An analytic method is presented which allows for the computation of the self-force for a static particle with a scalar charge in the region of an ultrastatic spacetime which one can call the long throat. The method is based on the approximate WKB solution of a radial mode equation for a scalar field. This field is assumed to be massless, with a coupling $\xi$ to the scalar curvature is satisfying the condition $\xi>1/8$.