Asymptotics of radiation fields in asymptotically Minkowski space

Abstract

We consider a non-trapping $n$-dimensional Lorentzian manifold endowed with an end structure modeled on the radial compactification of Minkowski space. We find a full asymptotic expansion for tempered forward solutions of the wave equation in all asymptotic regimes. The rates of decay seen in the asymptotic expansion are related to the resonances of a natural asymptotically hyperbolic problem on the "northern cap" of the compactification. For small perturbations of Minkowski space that fit into our framework, we show a rate of decay that improves on the Klainerman--Sobolev estimates.

67 pages, 2 figures; version 2 was a substantial revision with the main result (Theorem 1.1) improved; version 3 fixes a minor error in the iterative argument establishing the asymptotic expansion; version 4 includes a few cosmetic changes and adds a few references

References in corpus (1)

• Radiation field for Einstein vacuum equations with spacial dimension $n\ge 4$

Cited by in corpus (6)

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• A Vector Field Method for Non-Trapping, Radiating Spacetimes
• Feynman propagators and Hadamard states from scattering data for the Klein-Gordon equation on asymptotically Minkowski spacetimes