Price's Law for Spherically Symmetric Charged Black Holes
- Quinten Rutgers (MPI MiS, Leipzig)
Abstract
In recent years there has a been a lot of interest in proving late-time asymptotics results for black hole spacetimes. This is for example motivated by the strong cosmic censorship conjecture where the so-called "Price's law" along the event horizon of the black hole would give information about the extendibility properties of the inner Cauchy horizon. In this talk we will present work on the late-time asymptotics for the Einstein-Maxwell-scalar field system in spherical symmetry. This system serves as a nonlinear toy model for the vacuum Einstein equation outside of symmetry. The goal of this work is to prove late-time tails in the entire black hole exterior for the scalar field, as well as higher order derivatives. This relies on energy estimates using vector field multipliers and commutators, where the timelike Kodama vector field is particularly important for proving decay.