Princeton University Gravity Initiative Seminar
On the uniqueness of Kerr-de Sitter
Abstract: The uniqueness of the Kerr-de Sitter family of black hole spacetimes as stationary solutions to the Einstein vacuum equations is a crucial ingredient to understanding the final states of positive cosmological constant universes, such as our physical universe. In the asymptotically flat case, Kerr was shown to be the unique analytic stationary solution to the Einstein vacuum equations via a combination of results by Hawking, Carter, and Robinson. Outside of analyticity, Alexakis, Ionescu, and Klainerman showed several conditional C^\infty rigidity results for Kerr. In this talk, I will discuss some recent work in the spirit of Alexakis, Ionescu, and Klainerman showing the uniqueness of the stationary region of Kerr-de Sitter within the smooth class of stationary solutions to the Einstein vacuum equations with a positive cosmological constant.