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The wave equation on the Schwarzschild metric. II: Local decay for the spin-2 Regge-Wheeler equation. (English) Zbl 1076.58020

Summary: Odd-type spin-2 perturbations of Einstein’s equation can be reduced to the scalar Regge-Wheeler equation. We show that the weighted norms of solutions are in \(L^2\) of time and space. This result uses commutator methods and applies uniformly to all relevant spherical harmonics.

MSC:

58J45 Hyperbolic equations on manifolds
35Q75 PDEs in connection with relativity and gravitational theory
83C15 Exact solutions to problems in general relativity and gravitational theory
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References:

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