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In 4-dimensional General Relativity, there are several theorems restrictingthe topology of the event horizon of a black hole. In the stationary case,black holes must have a spherical horizon, while a toroidal spatial topology isallowed only for a short time. In this paper, we consider spinning black holesinspired by Loop Quantum Gravity and by alternative theories of gravity. Weshow that the spatial topology of the event horizon of these objects changeswhen the spin parameter exceeds a critical value and we argue that thephenomenon may be quite common for non-Kerr black holes. Such a possibility maybe relevant in astrophysics, as in some models the accretion process can inducethe topology transition of the horizon.

Can an astrophysical black hole have a topologically non-trivial event horizon?