Distinguishing the Observational Signatures of Hot Spots Orbiting Reissner-Nordstr\"om Spacetime

Abstract

This paper delves into observable signatures of hot spots orbiting Reissner-Nordstr\"om (RN) black holes and naked singularities. In a RN black hole case, we find two discernible lensing image tracks in time integrated images capturing a complete orbit of hot spots, and a image shadow within the critical curve where photons with a small impact parameter fall into the event horizon. Conversely, in RN singularities, additional image tracks can be found inner the critical curve, originating from photons reflected by the infinitely high effective potential well. Moreover, we found incomplete and converge tracks from the time integrated images of hot spot orbiting RN singularities lacking of a photon sphere. The presence of these additional image tracks exerts a significant influence on temporal magnitudes at their local maxima, allowing us to differentiate between RN black holes and RN naked singularities.