Light rings on stationary axisymmetric spacetimes: Blind to the topology and able to coexist

It has been established that black hole (BH) spacetimes obeying some general set of assumptions always possess, at least, one light ring (LR) per rotation sense [Cunha and Herdeiro, Phys. Rev. Lett. 124, 181101 (2020)]. This theorem was originally established for asymptotically flat, stationary, axial symmetric, $1+3$-dimensional circular spacetimes harboring a nonextremal and topologically spherical Killing horizon. Following the mantra that a theorem is only as strong as its assumptions, in this work we extend this theorem to nontopologically spherical (toroidal) BHs and to spacetimes harboring more than one BH. As shown previously, we here show that each BH still contributes with, at least, one LR (per rotation sense).