Fluid figures of equilibrium orbiting Reissner-Nordström black holes and naked singularities

We study figures of equilibrium of barotropic fluid with uniform, nonvanishing, values of specific angular momentum in the gravitational field of the Reissner-Nordstr"om (RN) space-time. The RN metric describes the space-time of a charged, static, spherically symmetric source of gravity, which happens to be a naked singularity when the absolute value of charge, $Q$, exceeds the mass, $M$. We treat the general relativistic RN solution as a representative of a wider class of spherically symmetric space-times in various theories of gravity that admit a (``zero-gravity'') spherical surface on which a test particle can remain at rest. The mechanism through which an orbiting fluid could lose its angular momentum in the vicinity of this zero-gravity sphere is as yet unknown; the fluid may possibly not come to rest there. In the gravity of the RN naked singularity, all equipotential surfaces of bound fluid with nonvanishing angular momentum have the topology of a torus (or two), and each of them may be filled by fluid in hydrostatic equilibrium. Depending on the value of the angular momentum of the fluid, the tori are completely or partly outside the zero-gravity sphere, and the locus of maximum pressure is always outside that sphere. The equipotential surfaces of unbound fluid have the topology of cylinders extending to infinity that are conducive to jetlike outflows of the fluid. Unlike in the black hole case, rotating fluid in the RN naked singularity metric can never accrete onto the central source of gravity; if bound, it will orbit the singularity inside one of the tori, and if unbound, it will flow out to infinity. Some of the tori shapes may correspond to the images reconstructed from the Einstein Horizon Telescope observations of Sgr A* and M87.