General classification of charged test particle circular orbits in Reissner--Nordstr\"om spacetime

TL;DR

This paper classifies charged test particle circular orbits in Reissner-Nordström spacetime, revealing how orbit behavior varies with source and particle charge-to-mass ratios, and proposing potential ways to distinguish black holes from naked singularities.

Contribution

It provides a comprehensive classification of circular orbits for various charge-to-mass ratios in Reissner-Nordström spacetime, including black holes and naked singularities, highlighting key charge thresholds.

Findings

Identifies critical charge-to-mass ratios for black holes and naked singularities.

Shows orbit behavior depends drastically on source type and particle charge.

Proposes that orbit analysis can distinguish black holes from naked singularities.

Abstract

We investigate charged particles circular motion in the gravitational field of a charged mass distribution described by the Reissner-Nordstr\"om spacetime. We introduce a set of independent parameters completely characterizing the different spatial regions in which circular motion is allowed. We provide 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, analogue 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.