Seminar room (2.8.3), Physics Building
Mokdad Mokdad, University of Burgundy-Franche-Comté
Scattering in the interior of black holes and the cosmic censorship conjecture
Scattering theories are of large importance for many problems in General Relativity, and scattering in the interior of a black hole is particularly relevant in the context of the cosmic censorship conjecture and the related Cauchy horizon instability problem. The Cauchy horizon instability is thought to be directly linked to a notion of gravitational blue-shift at the horizon, which manifests itself as a blow-up in some observed quantity. By constructing the scattering channels, one aims to recover information about the behavior of the field near the horizons, where the instabilities might be seen as the unboundedness of the scattering operators (energy blow-up) or from the lack of regularity at the horizon of the propagating field (C^1-blow-up). In this talk I will present the recent development of the scattering theories in the interior black holes between the Cauchy horizon and the event horizon, and the various blow-up results. From a mathematical point of view, different fields exhibit contrasting scattering phenomena. For example, the scattering of linear waves is delicate and surprising breakdowns of scattering happens in generic situations.