  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.
