Decay of Maxwell Fields on Reissner-Nordstr{\o}m-de Sitter Black Holes

Understand

In this paper we use Morawetz estimates with geometric energy estimates -the so-called vector field method- to prove decay results for the Maxwell field in the static exterior region of the Reissner-Nordstr{\o}m-de Sitter black hole.

• We prove two types of decay: The first is a uniform decay of the energy of the Maxwell field on achronal hypersurfaces as the hypersurfaces approach timelike infinities.
• The second decay result is a pointwise decay in time with a rate of $t^{-1}$ which follows from local energy decay by Sobolev estimates.
• Both results are consequences of bounds on the conformal energy defined by the Morawetz conformal vector field.