A black hole uniqueness theorem

          @misc{ scivideos_PIRSA:10050027,
            doi = {10.48660/10050027},
            url = {https://pirsa.org/10050027},
            author = {Alexakis, Spyros},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {A black hole uniqueness theorem},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2010},
            month = {may},
            note = {PIRSA:10050027 see, \url{https://scivideos.org/index.php/pirsa/10050027}}
          }
          

Abstract

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