Hawking showed that each connected component of the event horizon of a stationary black hole in 4-dimensional general relativity has the topology of a 2-sphere. An interesting question is whether this is true even for time varying horizons.
Using the topological censorship theorem of Friedman, Schleich and Witt [Phys. Rev. Lett. 71, 1486 (1993)], we show that if the horizon is spherical even in a non-stationary spacetime, if the spacetime is orientable and the horizon topolgy is unchanging for long enough (roughly the light crossing time of the black hole). This result has since been improved by Chrusciel and Wald, who removed the restriction that the spacetime be orientable. This result places stringent bounds on the possible dynamics of black-holes, and this result is relevant to recent numerical work on toroidal black-hole horizons.