A simple proof of the recent generalisations of Hawking's black hole topology theorem

A key result in four dimensional black hole physics, since the early 1970s, is Hawking's topology theorem asserting that the cross-sections of an "apparent horizon", separating the black hole region from the rest of the spacetime, are topologically two-spheres. Later, during the 1990s, by applying a variant of Hawking's argument, Gibbons and Woolgar could also show the existence of a genus dependent lower bound for the entropy of topological black holes with negative cosmological constant. Recently Hawking's black hole topology theorem, along with the results of Gibbons and Woolgar, has been generalised to the case of black holes in higher dimensions. Our aim here is to give a simple self-contained proof of these generalisations which also makes their range of applicability transparent.