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

Abstract

We describe an expansion of the solution of the wave equation in the De Sitter - Schwarzschild metric in terms of resonances. The main term in the expansion is due to a zero resonance. The error term decays polynomially if we permit a logarithmic derivative loss in the angular directions and exponentially if we permit an small derivative loss in the angular directions.

arXiv comment22 pages, 5 figures

References in corpus (4)

• Uniform Decay of Local Energy and the Semi-Linear Wave Equation on Schwarzchild Space
• Decay of Solutions of the Wave Equation in the Kerr Geometry
• Improved decay rates with small regularity loss for the wave equation about a Schwarzschild black hole
• Semiclassical scattering amplitude at the maximum point of the potential

Cited by in corpus (5)

• On quasinormal modes of asymptotically anti-de Sitter black holes
• Wave decay on convex co-compact hyperbolic manifolds
• Strong Cosmic Censorship for a Scalar Field in a Born-Infeld-de Sitter Black Hole
• Asymptotics of solutions of the wave equation on de Sitter-Schwarzschild space
• The wave equation on asymptotically de Sitter-like spaces