# Mathematical Relativity Seminar

### Stability and instability in spherical symmetry of Reissner-Nordström black holes for the Einstein-Maxwell-Klein-Gordon model

Penrose’s Strong Cosmic Censorship Conjecture is one of the central problems of Mathematical General Relativity. Its proof for the Einstein-Maxwell-Uncharged-Scalar-Field (EMSF) model in spherical symmetry relies on the formation of a Cauchy horizon that is $C^0$ regular but $C^2$ singular for generic Cauchy data. EMSF model however only admits two-ended black holes, unlike its charged analogue that allows for one-ended black holes, relevant to the study of charged gravitational collapse in spherical symmetry. In this talk, I will present my work about spherically symmetric charged and massive scalar fields on black holes. This includes a study of the black hole interior, that relates the behaviour of fields on the event horizon to the formation of a $C^0$ regular and $C^2$ singular Cauchy horizon. I will also mention my more recent work on the black hole exterior stability, for weakly charged massless scalar fields.

Current organizers: José Natário, João Lopes Costa