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arXiv · 1701.06587

Upper bound on the radii of black-hole photonspheres

Shahar Hod
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Abstract

One of the most remarkable predictions of the general theory of relativity is the existence of black-hole "photonspheres", compact null hypersurfaces on which massless particles can orbit the central black hole. We prove that every spherically-symmetric asymptotically flat black-hole spacetime is characterized by a photonsphere whose radius is bounded from above by $r_{\gamma} \leq 3M$, where $M$ is the total ADM mass of the black-hole spacetime. It is shown that hairy black-hole configurations conform to this upper bound. In particular, the null circular geodesic of the (bald) Schwarzschild black-hole spacetime saturates the bound.

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Shahar Hod. 2017-01-23. Upper bound on the radii of black-hole photonspheres. https://doi.org/10.1016/j.physletb.2013.10.047

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