Stationary black holes and light rings. (arXiv:2003.06445v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Cunha_P/0/1/0/all/0/1">Pedro V. P. Cunha</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Herdeiro_C/0/1/0/all/0/1">Carlos A. R. Herdeiro</a>
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.
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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