Remarks on the geodesically completeness and the smoothing effect on asymptotically Minkowski spacetimes
Mathematical Physics
2022-03-23 v2 General Relativity and Quantum Cosmology
Analysis of PDEs
Differential Geometry
math.MP
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.
Keywords
Cite
@article{arxiv.2107.10509,
title = {Remarks on the geodesically completeness and the smoothing effect on asymptotically Minkowski spacetimes},
author = {Kouichi Taira},
journal= {arXiv preprint arXiv:2107.10509},
year = {2022}
}