- 6635 South Hall
In recent years there has been an explosion of interest in black holes in higher dimensional gravity. This, in particular, has led to questions about the topology of black holes in higher dimensions. In this talk we review Hawking's classical theorem on the topology of black holes in 3+1 dimensions (and its connection to black hole uniqueness) and present a generalization of it to higher dimensions. The latter is a geometric result which places restrictions on the topology of black holes in higher dimensions. We shall also discuss recent work on the topology of space exterior to a black hole. This is closely connected to the Principle of Topological Censorship, which roughly asserts that the topology of the region outside of all black holes (and white holes) should be simple. All of the results to be discussed rely on the recently developed theory of marginally outer trapped surfaces, which are natural spacetime analogues of minimal surfaces in Riemannian geometry. This talk is based primarily on joint work with Rick Schoen and with Michael Eichmair and Dan Pollack.