Fastest curves and toroidal black holes

We discuss an apparent paradox (and conjectured resolution) of Jacobson and Venkataramani concerning 'temporarily toroidal' black hole horizons, in light of a recent connectivity theorem for spaces of complete causal curves. We do this in a self-contained manner by first reviewing the 'fastest curve argument' which proves this connectivity theorem, and we note that active topological censorship can be derived as a corollary of this argument. We argue that the apparent paradox arises only when one dispenses with the invariant viewpoint provided by the connectivity theorem in favour of an observer-dependent description. Finally, we discuss an alternative to fastest curve arguments, which can be used to construct a self-contradictory null line in certain spacetimes violating topological censorship. These arguments may shed light on the relationship between topological and cosmic censorship.