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Stationary black holes and light rings

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arxiv 2003.06445 v1 pith:C37XU4FU submitted 2020-03-13 gr-qc astro-ph.HEhep-th

Pedro V. P. Cunha , Carlos A. R. Herdeiro This is my paper
classification gr-qcastro-ph.HEhep-th
keywords blackargumentholehorizonlightmustorbitsrings
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abstract

The ringdown and shadow of the astrophysically significant Kerr Black Hole (BH) are both intimately connected to a special set of bound null orbits known as Light Rings (LRs). Does it hold that a generic equilibrium BH must possess such orbits? In this letter we prove the following theorem. A stationary, axi-symmetric, asymptotically flat black hole spacetime in 1+3 dimensions, with a non-extremal, topologically spherical, Killing horizon admits, at least, one standard LR outside the horizon for each rotation sense. The proof relies on a topological argument and assumes $C^2$-smoothness and circularity, but makes no use of the field equations. The argument is also adapted to recover a previous theorem establishing that a horizonless ultra-compact object must admit an even number of non-degenerate LRs, one of which is stable.

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Cited by 5 Pith papers

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