Equilibrium tori orbiting Reissner-Nordstr\"om naked singularities

Abstract

In general relativity, the asymptotically flat space-time of a charged, spherically symmetric (non-rotating) body is described by the Reissner-Nordstr\"om metric. This metric corresponds to a naked singularity when the absolute value of charge, \(Q\), exceeds the mass, \(M\). For all Reissner-Nordstr\"om naked singularities, there exists a zero gravity sphere where a test particle can remain at rest. Outside that sphere gravity is attractive, inside it gravity is repulsive. For values of \(Q/M>\sqrt{9/8}\) the angular frequency of circular test-particle orbits has a maximum at radius \(r=(4/3)\,Q^2/M\). We construct polytropic tori with uniform values of specific angular momentum in the naked singularity regime of the Reissner-Nordstr\"om metric, \((Q/M>1)\).