Paper
The asymptotics of massive fields on stationary spherically symmetric black holes for all angular momenta
Authors
Federico Pasqualotto, Yakov Shlapentokh-Rothman, Maxime Van de Moortel
Abstract
We study the massive scalar field equation on a stationary and spherically symmetric black hole (including in particular the Schwarzschild and Reissner--Nordström black holes in the full sub-extremal range) for solutions projected on a fixed spherical harmonic. Our problem involves the scattering of an attractive long-range potential (Coulomb-like) and thus cannot be treated perturbatively.
We prove precise (point-wise) asymptotic tails of the form , where is an explicit oscillating profile. Our asymptotics appear to be the first rigorous decay result for a massive scalar field on a black hole. Establishing these asymptotics is also an important step in retrieving the assumptions used in work of the third author regarding the interior of dynamical black holes and Strong Cosmic Censorship.