Equilibrium tori orbiting Reissner-Nordström naked singularities

In general relativity, the asymptotically flat space-time of a charged, spherically symmetric (non-rotating) body is described by the Reissner-Nordström metric. This metric corresponds to a naked singularity when the absolute value of charge, $Q$, exceeds the mass, $M$. For all Reissner-Nordström 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 $Q\mathrm{/}M>\sqrt{9\mathrm{/}8}$ the angular frequency of circular test-particle orbits has a maximum at radius $r=(4\mathrm{/}3)Q^2\mathrm{/}M$. We construct polytropic tori with uniform values of specific angular momentum in the naked singularity regime of the Reissner-Nordström metric, $(Q\mathrm{/}M>1)$.