Room P3.10, Mathematics Building

Flavio Rossetti

Flavio Rossetti, Instituto Superior Técnico
The entire universe in one flash: on the stability of the Cauchy horizon for cosmological black holes in spherical symmetry

We discuss the problem of global uniqueness for the Einstein equations with a positive cosmological constant. After reviewing the modern formulations of strong cosmic censorship (SCCC), we prove a stability result suggesting a potential failure of SCCC in the spherically symmetric framework. In particular, we study the characteristic initial value problem (IVP) for the spherically symmetric Einstein-Maxwell-charged-Klein-Gordon system, with initial data as expected to arise from charged gravitational collapse. The solution to the IVP describes the interior of a black hole asymptotically approaching a sub-extremal Reissner-Nordström-de Sitter spacetime. By using bootstrap methods in the black hole interior, we establish the $H^1$ non-linear stability of the Cauchy horizon for a large set of initial data.