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In the final chapter of this book, we set off a little microlocal firework by combining almost all of the microlocal tools we have developed in order to give a precise description of the asymptotic (late-time) behavior of solutions of linear wave-type equations on a spacetime of interest in general relativity—de Sitter space , more precisely, a neighborhood of the static patch of de Sitter space. We describe this spacetime and the null-geodesic flow on it in Section 11.1. We then state the main results in Section 11.2 and sketch their proofs. The details of the proofs are given in Sections 11.3–11.5. We describe a simple nonlinear application in Section 11.6.

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Late-Time Asymptotics of Linear Waves on de Sitter Space

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  • 发表日期：

    2025年

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  • Peter Hintz

摘要

In the final chapter of this book, we set off a little microlocal firework by combining almost all of the microlocal tools we have developed in order to give a precise description of the asymptotic (late-time) behavior of solutions of linear wave-type equations on a spacetime of interest in general relativity—de Sitter space , more precisely, a neighborhood of the static patch of de Sitter space. We describe this spacetime and the null-geodesic flow on it in Section 11.1. We then state the main results in Section 11.2 and sketch their proofs. The details of the proofs are given in Sections 11.3–11.5. We describe a simple nonlinear application in Section 11.6.