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Uniform boundedness and continuity at the Cauchy horizon for linear waves on Reissner--Nordström--AdS black holes

Banff International Research Station for Mathematical Innovation and Discovery

I will present a recent result on solutions to the massive linear wave equation $\Box_g \psi - \mu \psi =0$ on the interior of Reissner--Nordström--AdS black holes. This is motivated by the Strong Cosmic Censorship Conjecture for asymptotically AdS black holes with negative cosmological constant $\Lambda <0$. Our main result shows that linear waves arising from a spacelike hypersurface with Dirichlet (reflecting) boundary conditions imposed at infinity remain bounded in the interior and can be extended continuously beyond the Cauchy horizon. This result is surprising because in contrast to black hole backgrounds with non-negative cosmological constant, the decay of $\psi$ in the exterior region for asymptotically AdS black holes is only logarithmic (cf. polynomial ($\Lambda =0$) and exponential ($\Lambda >0$)).

Mathematics; Relativity and gravitational theory; Partial differential equations; Global analysis

video/mp4

Author affiliation: Cambridge

2020-01-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73413

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/