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Equilibrium tori orbiting Reissner-Nordstr\"om naked singularities
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abstract
In general relativity, the asymptotically flat space-time of a charged, spherically symmetric (non-rotating) body is described by the Reissner-Nordstr\"om metric. This metric corresponds to a naked singularity when the absolute value of charge, $Q$, exceeds the mass, $M$. For all Reissner-Nordstr\"om 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 $Q/M>\sqrt{9/8}$ the angular frequency of circular test-particle orbits has a maximum at radius $r=(4/3)\,Q^2/M$. We construct polytropic tori with uniform values of specific angular momentum in the naked singularity regime of the Reissner-Nordstr\"om metric, $(Q/M>1)$.
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Periodic orbits of neutral test particles in Reissner-Nordstr\"{o}m naked singularities
For Reissner-Nordström naked singularities, each rational periodic orbit in the outer region can share the same energy and angular momentum with an inner-region periodic orbit, and the full (L,E) atlas is divided into...
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