  It has been established that Black Hole (BH) spacetimes obeying some general
set of assumptions always possess, at least, one light ring (per rotation
sense) [arXiv:2003.06445]. This theorem was originally established for
asymptotically flat, stationary, axial symmetric, 1+3 dimensional circular
spacetimes harbouring a non-extremal 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 non topologically spherical
(toroidal) BHs and to spacetimes harbouring more than one BH. As in
[arXiv:2003.06445], we show that each BH still contributes with, at least, one
LR (per rotation sense).
