Self-force on charges in the spacetime of spherical shells

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 scaler 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.