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Asymptotics of radiation fields in asymptotically Minkowski space
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 137, Number 5, October 2015
- pp. 1293-1364
- 10.1353/ajm.2015.0033
- Article
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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, our asymptotic expansions yield a rate of decay that improves on the Klainerman-Sobolev estimates.