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N. N

Alessandra Tullini (WWU): Energy blowup of linear waves near the Cauchy horizon of Reissner?Nordström?AdS. Oberseminar Topics in General Relativity

Tuesday, 13.12.2022 12:00 im Raum 503

Mathematik und Informatik

Reissner?Nordström?Anti-de Sitter spacetimes are black hole solutions to the Einstein-Maxwell system of equations under the assumption of a negative cosmological constant. They present with a Cauchy horizon and are thus of interest in the context of Strong Cosmic Censorship Conjecture. In a series of works, Kehle addressed the linear formulation of the conjecture in RN-AdS, which involves the study of the initial value problem for Klein-Gordon?s equation. In 2019, he proved uniform boundedness and continuity of solutions emanating from a spacelike hypersurface and satisfying Dirichlet boundary conditions, thus disproving the C0 formulation. In 2021, under the same boundary conditions, he recovered the H1 formulation by identifying a class of initial data whose resulting solution presents with unbounded local energy near the Cauchy horizon. We focus on the latter work and shine a light onto the identification of such a class and on the notion of genericity thus associated. The argument rests on the possibility of finding a quasi normal mode solution with unbounded local energy near the Cauchy horizon. Then, because of the linear nature of the problem, we may perturb any initial data (among those for which we have well-posedness) with initial data for the QNM exhibiting energy blowup and still obtain (local) energy blowup. The blowup behaviour is generic in the following sense: the set of initial data such that the resulting solution has bounded local energy near the Cauchy horizon, is at most a codimension 1 subset of the set of all admissible initial data. In conclusion, under this notion of genericity, the linear H1 formulation of the conjecture is restored in RN-AdS.



Angelegt am Monday, 05.12.2022 10:24 von N. N
Geändert am Thursday, 08.12.2022 13:56 von N. N
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