  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. These bounds are obtained through wave
analysis on the middle spin component of the field. The results hold for a more
general class of spherically symmetric spacetimes with the same arguments used
in this paper.
