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Equilibrium tori orbiting Reissner-Nordström naked singularities

In a remarkable study, Abramowicz, Jaroszyński, and Sikora (1978) computed the hydrodynamical structure of an accretion disk orbiting a black hole. There are closed and open equipotential surfaces and a fluid in hydrostatic equilibrium can occupy the volume within any of the closed surfaces. Near the black hole the gravity is so strong that the equipotential surfaces can self-intersect forming a cusp, often referred to as Sikora’s beak, through which fluid can spill onto the black hole. The topology of these equipotential surfaces makes it hard for the accreting fluid to flow (and escape) in the vertical (axial) direction. One needs factors different from gravity to force any sort of outflow along the axis of symmetry.

Surprisingly, this is not the case when the event horizon is absent. The recent paper “Equilibrium tori orbiting Reissner-Nordstrom naked singularities” by Ruchi Mishra and Włodek Kluźniak from the Copernius Astronomical Center in Warsaw, shows what happens when one considers fluid bodies in hydrostatic equilibrium orbiting a Reissner-Nordström naked singularity. The Reissner-Nordström metric is an exact solution of Einstein’s vacuum equations describing a spherically symmetric electrically charged source of gravity. It allows both black holes and naked singularities (depending on the mass to electric charge ratio). Contrary to the black hole case, for a naked singularity, even if the electrically neutral fluid gains sufficient energy to spill from the volume within a closed equipotential surface, it will only barely approach the central singularity. Instead of being captured by the singularity, the fluid will outflow to infinity in the quasi-axial direction, following the open equipotential surfaces by the action of gravity and pressure alone.


Figure caption: Left panel: A figure adopted from Abramowicz, Jaroszyński, and Sikora (1978) showing equipotential surfaces around a black hole. The presence of the cusp allows the accretion onto the black hole without losing angular momentum. Right panel: Equipotential surfaces around Reissner-Nordström naked singularity with charge to mass ratio Q = 1.8.


Text: Ruchi Mishra