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We consider solutions to the linear wave equation $\Box_g\phi=0$ on a non-extremal maximally extended Schwarzschild-de Sitter spacetime arising from arbitrary smooth initial data prescribed on an arbitrary Cauchy hypersurface.
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P. R. Brady, C. M. Chambers, W. G. Laarakkers, and E. Poisson Radiative falloff in Schwarzschild-de Sitter spacetime Phys. Rev. D 60
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P. Blue and A. Soffer Errata for “Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds”, “Semilinear wave equations on the Schwarzschild manifold I: Local Decay Estimates”, and “The wave equation on the Schwarzschild metric II: Local Decay for the spin 2 Regge Wheeler equation” , gr-qc/0608073, 6 pages
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M. Dafermos and I. Rodnianski A note on boundary value problems for black hole evolution , gr-qc/0403034
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M. Dafermos and I. Rodnianski The redshift effect and radiation decay on black hole spacetimes , gr-qc/0512119
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J.-F. Bony and D. Häfner Decay and non-decay of the local energy for the wave equation in the de Sitter-Schwarzschild metric , preprint 2007
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