Gravitational lensing by a photon sphere in a Reissner-Nordstr\"{o}m naked singularity spacetime in strong deflection limits

TL;DR

This paper analytically studies gravitational lensing effects near a photon sphere in a Reissner-Nordström naked singularity spacetime, revealing distinctive image brightness features that differentiate it from black hole spacetimes.

Contribution

It provides explicit analytic expressions for deflection angles in strong deflection limits without Taylor expansions, and identifies observable differences between naked singularities and black holes.

Findings

Infinite images can form near the photon sphere due to potential barriers.

Images inside the photon sphere are brighter in naked singularity spacetimes.

Distinct brightness patterns can distinguish naked singularities from black holes.

Abstract

We investigate gravitational lensing by a photon sphere in a Reissner-Nordstr\"{o}m 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-Nordstr\"{o}m 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.