General classification of charged test particle circular orbits in Reissner\u2013Nordstr\xf6m spacetime

Abstract

We investigate charged particles’ circular motion in the gravitational field of a charged mass distribution described by the Reissner–Nordström spacetime. We introduce a set of independent parameters completely characterizing the different spatial regions in which circular motion is allowed. We provide a most complete classification of circular orbits for different sets of particle and source charge-to-mass ratios. We study both black holes and naked singularities and show that the behavior of charged particles depend drastically on the type of source. Our analysis shows in an alternative manner that the behavior of circular orbits can in principle be used to distinguish between black holes and naked singularities. From this analysis, special limiting values for the dimensionless charge of black hole and naked singularity emerge, namely, Q/M = 1/2, Q/M=sqrt{13}/5 and Q/M=sqrt{2/3} for the black hole case and Q/M = 1, Q/M=5/ (2 sqrt{6}), Q/M=3 sqrt{6}/7, and finally Q/M= sqrt{9/8} for the naked singularity case. Similarly and surprisingly, analogous limits emerge for the orbiting particles charge-to-mass ratio epsilon , for positive charges epsilon =1, epsilon =2 and epsilon =M/Q. These limits play an important role in the study of the coupled electromagnetic and gravitational interactions, and the investigation of the role of the charge in the gravitational collapse of compact objects.