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Asymptotics of radiation fields in asymptotically Minkowski space
- Publication Year :
- 2012
-
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.<br />Comment: 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
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1212.5141
- Document Type :
- Working Paper