A black hole uniqueness theorem.

2 June 2009
Spyridon Alexakis
I will discuss recent joint work with A. Ionescu and S. <br /> Klainerman on the black hole uniqueness problem. A classical result of <br /> Hawking (building on earlier work of Carter and Robinson) asserts that any <br /> vacuum, stationary black hole exterior region must be isometric to the <br /> Kerr exterior, under the restrictive assumption that the space-time metric <br /> should be analytic in the entire exterior region.<br /> We prove that Hawking's theorem remains valid without the assumption of <br /> analyticity, for black hole exteriors which are apriori assumed to be &quot;close&quot;<br /> to the Kerr exterior solution in a very precise sense. Our method of proof <br /> relies on certain geometric Carleman-type estimates for the wave operator.