From a purely geometric (kinematic) perspective, black holes in four
dimensional spacetimes can have event horizons with arbitrary topologies. It is
only when energy conditions are imposed that the horizon’s shape is constrained
to be spherical. Despite this, exploring exotic horizon topologies remains
theoretically intriguing since it allows to unveil structural aspects of
General Relativity and gain intuition on energy condition violations. In the
axisymmetric case, besides the well-known spherical topology, only a toroidal
topology is consistent with the symmetry. Complete solutions, describing the
entire exterior region of such toroidal black holes without singularities, have
not been reported yet. To the best of our knowledge, the construction we
present here is the first explicit example of a toroidal black hole solution in
four spacetime dimensions that is free of singularities in the external region.

Questo articolo esplora i giri e le loro implicazioni.

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