Dominic Dold (University of Cambridge): The Black Hole Uniqueness Problem for Negative Cosmological Constant

Abstract: It is a long-standing conjecture that every asymptotically flat stationary black hole solution to the Einstein vacuum equations is a member of the Kerr family. The full problem is still open, but under the assumption of axial symmetry, uniqueness has been shown by Carter and Robinson (1971/1975). In the first part of my talk, I will motivate the set-up of this problem and review some classical approaches. The second part will deal with the problems one faces when attempting to generalise these approaches to the Einstein vacuum equations with negative cosmological constant.