Joint Online Mathematical Relativity Colloquium: Elena Giorgi (Seminar)

Thursday 1 December 2022Add to my calendar
15:30 to
HG03.761 and zoom (see link in description)
Elena Giorgi (Columbia University)
Physical-space estimates on black hole perturbations

Most works on the analysis of the wave equation on Kerr black holes rely on a combination of the vector field method and Fourier decomposition, with the notable exception of a generalized vector field method introduced by Andersson-Blue. Their method allows for commutation with second order differential operators entirely in physical-space by supplementing the Killing vector fields with the Carter operator of Kerr to obtain a local energy decay identity at the level of three derivatives of the solution for sufficiently small |a|. I this talk I will describe the main ideas of Andersson-Blue's method and explain its advantages in two recent applications where physical space-estimates have been crucial: the linear stability of Kerr-Newman black hole to coupled gravitational-electromagnetic perturbations and our proof of the non-linear stability of the slowly rotating Kerr family with Klainerman-Szeftel.

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Annegret Burtscher