The spacelike-characteristic Cauchy problem with bounded L2 curvature in general relativity

Jeudi 2 juillet 11:00-12:00 - Olivier Graf - Laboratoire Jacques-Louis Lions

Résumé : In this talk I will review the classical Cauchy problem for
Einstein equations. I will explain some of its geometric features and
recast the equations as a system of coupled quasilinear
transport-elliptic-Maxwell equations. I will present the global-in-time
existence conjecture (aka the conjecture of weak cosmic censorship) and
how low regularity local existence results (as the celebrated bounded L2
curvature theorem) can be used to get insight on the formation of
singularities. I will then review the classical bounded L2 curvature
theorem of Klainerman-Rodnianski-Szeftel and present a version
generalised to initial data posed on an initial spacelike and an initial
characteristic hypersurface that I obtained jointly with Stefan Czimek.
The talk will be in English and presented purely from a PDEist perspective.

Notes de dernières minutes : Exposé en visio, le lien sera disponible la semaine précédent l’exposé.

The spacelike-characteristic Cauchy problem with bounded L2 curvature in general relativity  Version PDF