Self force of a static electric charge near a Schwarzschild Star

TL;DR

This paper derives the self-force on a static electric charge near a Schwarzschild star, revealing that the force can be attractive or repulsive depending on the star's properties and the charge's position, differing from black hole scenarios.

Contribution

It provides explicit formulas for the self-force near both insulating and conducting Schwarzschild stars, including the extreme density case, and shows the force's dependence on star properties and charge position.

Findings

Self-force is repulsive near an insulating Schwarzschild star.

For a conducting star, the force can be attractive or repulsive depending on distance.

Far from the star, the force matches that near a black hole of the same mass.

Abstract

When a charge is held static near a constant density spherical star, it experiences a self-force which is significantly different from the force it would experience when placed near a black hole of the same mass. In this paper, an expression for the self-force (as measured by a locally inertial observer) is given %explicitly calculated for an insulating Schwarzschild star, and the result is explicitly computed for the extreme density case, which has a singularity at its center. The force is found to be repulsive. A similar calculation of the self-force is also performed for a conducting star. This calculation is valid for any static, spherically conducting star, since the result is independent of the interior metric. When the charge is placed very close to the conducting star, the force is found to be attractive but when the charge is placed beyond a certain distance (2.95M for a conducting star of radius 2.25M), the force is found to be repulsive. When the charge is placed very far from the star (be it conducting or insulating), the charge experiences the same repulsive force it would experience when placed in the spacetime of a black hole with the same mass as the star.