Asymptotics of solutions of the wave equation on de Sitter-Schwarzschild space

Abstract

Solutions to the wave equation on de Sitter-Schwarzschild space with smooth initial data on a Cauchy surface are shown to decay exponentially to a constant at temporal infinity, with corresponding uniform decay on the appropriately compactified space.

References in corpus (1)

• Decay and non-decay of the local energy for the wave equation in the De Sitter - Schwarzschild metric

Cited by in corpus (9)

• A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds
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• A scattering theory construction of dynamical vacuum black holes
• Global results for linear waves on expanding Kerr and Schwarzschild de Sitter cosmologies
• Effective limiting absorption principles, and applications
• Decay properties of Klein-Gordon fields on Kerr-AdS spacetimes
• The wave equation on asymptotically Anti-de Sitter spaces
• Analytic continuation and semiclassical resolvent estimates on asymptotically hyperbolic spaces
• Linear Instability of the Reissner-Nordström Cauchy Horizon