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- W4298277109 abstract "This paper establishes that on the domain of outer communications of a general class of stationary and asymptotically flat Lorentzian manifolds of dimension $d+1$, $dge3$, the local energy of solutions to the scalar wave equation $square_{g}psi=0$ decays at least with an inverse logarithmic rate. This class of Lorentzian manifolds includes (non-extremal) black hole spacetimes with no restriction on the nature of the trapped set. Spacetimes in this class are moreover allowed to have a small ergoregion but are required to satisfy an energy boundedness statement. Without making further assumptions, this logarithmic decay rate is shown to be sharp. Our results can be viewed as a generalisation of a result of Burq, dealing with the case of the wave equation on flat space outside compact obstacles, and results of Rodnianski--Tao for asymptotically conic product Lorentzian manifolds. The proof will bridge ideas of Rodnianski--Tao with techniques developed in the black hole setting by Dafermos--Rodnianski. As a soft corollary of our results, we will infer an asymptotic completeness statement for the wave equation on the spacetimes considered, in the case where no ergoregion is present." @default.
- W4298277109 created "2022-10-01" @default.
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- W4298277109 date "2015-09-28" @default.
- W4298277109 modified "2023-10-17" @default.
- W4298277109 title "Logarithmic local energy decay for scalar waves on a general class of asymptotically flat spacetimes" @default.
- W4298277109 doi "https://doi.org/10.48550/arxiv.1509.08495" @default.
- W4298277109 hasPublicationYear "2015" @default.
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