Gravitational lensing by a photon sphere in a Reissner-Nordstrom naked singularity spacetime in strong deflection limits

We investigate gravitational lensing by a photon sphere in a Reissner-Nordstrom naked singularity spacetime in strong deflection limits. Because of the nonexistence of an event horizon and the existence of a potential barrier near an antiphoton sphere, infinite numbers of images slightly inside and outside of a photon sphere can appear. We obtain the analytic expressions of the factors of logarithmic divergent terms and the constant terms of the deflection angles in the strong deflection limits not only the for the little outside but also the barely inside of the photon sphere without Taylor expansions in the power of an electric charge. We can distinguish between a Reissner-Nordstrom black hole spacetime and the naked singularity spacetime since the images little inside of the photon sphere around the naked singularity are significantly brighter than the image barely outside of the photon sphere around the black hole and the naked singularity.

Automated summary

In the strong deflection limit, gravitational lensing by a photon sphere in a Reissner-Nordstrom naked singularity spacetime can result in an infinite number of images with significantly different brightness levels around the photon sphere. By studying the analytic expressions of the deflection angles, it is possible to distinguish between a black hole spacetime and a naked singularity spacetime.