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

Understand

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.