Effects of a modified Reissner-Nordström spacetime

Abstract

A modified Reissner-Nordström spacetime is considered here, where the central object (for example, a black hole or naked singularity) possesses a mass, with an “ordinary”, i.e., Standard Model (SM) electric charge, along with a “dark” electric charge associated with dark matter (DM). The inclusion of this dark charge modifies the gravitational properties of the spacetime, while not affecting ordinary electrodynamics. Geodesic motions of both charged and uncharged SM test particles are modified due to the presence of dark charge. The modifications may allow the detection and measrement of the dark charge. In particular, (1) the effective potential for orbiting particles is modified, and consequently, (2) the angular momenta and ISCOs of test masses in circular orbits are changed from those for the usual Reissner-Nordström case. (3) In the case of a naked singularity, it is possible that a “levitating atmosphere”, due to short distance repulsive gravity, forms at the zero gravity radius, which depends upon both SM and DM charges. A levitating atmosphere may then cloak the naked singularity.