Self force of a static electric charge near a Schwarzschild Star

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.