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arXiv · 1201.0068

The fastest way to circle a black hole

Shahar Hod
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Abstract

Black-hole spacetimes with a "photonsphere", a hypersurface on which massless particles can orbit the black hole on circular null geodesics, are studied. We prove that among all possible trajectories (both geodesic and non-geodesic) which circle the central black hole, the null circular geodesic is characterized by the {\it shortest} possible orbital period as measured by asymptotic observers. Thus, null circular geodesics provide the fastest way to circle black holes. In addition, we conjecture the existence of a universal lower bound for orbital periods around compact objects (as measured by flat-space asymptotic observers): $T_{\infty}\geq 4\pi M$, where $M$ is the mass of the central object. This bound is saturated by the null circular geodesic of the maximally rotating Kerr black hole.

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Shahar Hod. 2011-12-30. The fastest way to circle a black hole. https://doi.org/10.1103/physrevd.84.104024

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