Retrolensing by light rays slightly inside and outside of a photon sphere around a Reissner-Nordstr\"{o}m naked singularity

Abstract

We investigate retrolensing of sunlights reflected by a photon sphere and by a potential barrier near an antiphoton sphere around a Reissner-Nordstr\"{o}m naked singularity. We apply the deflection angles of light rays in strong deflection limits to the retrolensing. We show that the retrolensing by the photon sphere around the Reissner-Nordstr\"{o}m naked singularity can be brighter than the one around a Reissner-Nordstr\"{o}m black hole because of the existence of the rays which reflected by the potential barrier.