Electrostatic self-force of a point charge in non rotating BTZ geometries

In the present paper it is studied the electrostatic of charges in non rotating BTZ black holes and wormholes. The particularities of the geometry makes the analysis considerable more complicated than usual electrostatic in a flat geometry. First, these space times are not asymptotically flat but instead asymptotically AdS. In addition, the relative distance d(r, r+ 1) between two particles located at a radius r and r + 1 in the geometry tends to zero when r → ∞. This behavior, which is radically different in a flat geometry, changes the analysis of the asymptotic conditions for the electrostatic field. These subtleties are carefully analyzed in the paper. In addition the self-interaction for a static point charge is calculated in a series expansion in a BTZ black hole and also in an wormhole constructed connecting two identical BTZ geometries. The electrostatic self-force is evaluated numerically and compared in both cases. The differences between the self force in both cases is a theoretical experiment for distinguishing both geometries, which otherwise are locally indistinguishable.