Self force on charges in the spacetime of spherical shells

TL;DR

This paper investigates the self force on static electric and scalar charges near spherical shells, revealing that the force is repulsive and depends on the shell's mass, with new corrections for finite shell size.

Contribution

It applies the Mode Sum Regularization Prescription to compute self forces, providing new insights into their dependence on shell mass and size, and correcting previous zero or inverse-cubic force laws.

Findings

Self force is always repulsive.

Scalar force is quadratic in shell mass, a second post-Newtonian effect.

Electric force is linear in shell mass, a first post-Newtonian effect.

Abstract

We study the self force acting on static electric or scalar charges inside or outside a spherical, massive, thin shell. The regularization of the self force is done using the recently-proposed Mode Sum Regularization Prescription. In all cases the self force acting on the charge is repulsive. We find that in the scalar case the force is quadratic in the mass of the shell, and is a second post-Newtonian effect. For the electric case the force is linear in the shell's mass, and is a first post-Newtonian effect. When the charge is outside the shell our results correct the known zero self force in the scalar case or the known repulsive, inverse-cubic force law in the electric case, for the finite size of the shell. When the charge is near the center of the shell the charge undergoes harmonic oscillations.