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arXiv · 2107.10509

Remarks on the geodesically completeness and the smoothing effect on asymptotically Minkowski spacetimes

Kouichi Taira
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Abstract

In this note, we study a geometric property of asymptotically Minkowski spacetimes and an analytic property of the Klein-Gordon operator. Precisely, our first main results show that asymptotically Minkowski spacetimes are geodesically complete under a null non-trapping condition. Secondly, we prove that Sobolev index of a real principal type estimate used in the previous work is actually optimal.

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Kouichi Taira. 2021-07-22. Remarks on the geodesically completeness and the smoothing effect on asymptotically Minkowski spacetimes. https://doi.org/10.1007/s11005-022-01517-2

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