Abstract:
Consider a non-rotating spherically symmetric charged black hole with mass M>0 and a charge Q\neq 0, in a de Sitter background of positive curvature (\Lambda>0). Taking solutions to geometric wave equations on the exterior region of this black hole, we use a physical-space-based method for deriving the leading-order late-time behaviour of integrated local energy decay estimates of solutions.
These estimates could be used for deriving the precise leading-order late-time behaviour of asymptotics and energy decay. Our method relies on exploiting the spatial decay properties of time integrals of solutions. With them, we are able to derive the existence and precise genericity properties of energy of the solutions and obtain uniform decay estimates of local energy in time.