General upper limit on the electric charge of Sgr A* in the Reissner–Nordström metric

Abstract

ABSTRACT In general relativity, the gravitational field of an electrically charged, non-rotating, spherically symmetric body is described by the Reissner–Nordström (RN) metric. Depending on the charge to mass ratio, the solution describes a black hole or a naked singularity. In the naked-singularity regime, a general property of this metric is the existence of a radius, known as the zero-gravity radius, where a test particle would remain at rest. As a consequence of repulsive gravity there is no circular orbit inside this radius, and at least a part of any quasi-stable structure must necessarily lie outside of it. Assuming the iconic torus in the compact source Sgr A* at the Galactic centre observed by the Event Horizon Telescope (EHT) to be the image of a quasi-stationary fluid structure, we provide rigorous constraints in the RN metric on the electric charge-to-mass ratio Q/M of Sgr A*. A comparison between the EHT observations and the space–time zero-gravity radius provides the most conservative limit on the charge of Sgr A* to be |Q/M| < 2.32 in geometrized units. A charged naked singularity respecting this charge-to-mass constraint is consistent with the current EHT observations, if the image is not interpreted as a photon ring.