Title: Decay of Solutions to the Maxwell Equations on Schwarzschild-de Sitter Spacetimes,
Abstract: In this work, we consider solutions of the Maxwell equations on the
Schwarzschild-de Sitter family of black hole spacetimes. We prove that, in the
static region bounded by black hole and cosmological horizons, solutions of the
Maxwell equations decay to stationary Coulomb solutions at a super-polynomial
rate, with decay measured according to ingoing and outgoing null coordinates.
Our method employs a differential transformation of Maxwell tensor components
to obtain higher-order quantities satisfying a Fackerell-Ipser equation, in the
style of Chandrasekhar and the more recent work of Pasqualotto. The analysis of
the Fackerell-Ipser equation is accomplished by means of the vector field
method, with decay estimates for the higher-order quantities leading to decay
estimates for components of the Maxwell tensor.