Self-force as a probe of global structure

Abstract

We calculate the self-force on an electric charge and electric dipole held at rest in a closed universe that results from joining two copies of Minkowski spacetime at a common boundary. Spacetime is strictly flat on each side of the boundary, but there is curvature at the surface layer required to join the two Minkowski spacetimes. We find that the self-force on the charge is always directed away from the surface layer. This is analogous to the case of an electric charge held at rest inside a spherical shell of matter, for which the self-force is also directed away from the shell. For the dipole, the direction of the self-force is a function of the dipole's position and orientation. Both self-forces become infinite when the charge or dipole is made to approach the surface layer. This study reveals that a self-force can arise even when the Riemann tensor vanishes at the position of the charge or dipole; in such cases the self-force is a manifestation of the global curvature of spacetime.