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

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.

References in corpus (3)

• Feynman Propagators on Static Spacetimes
• An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime
• Limiting absorption principle and equivalence of Feynman propagators on asymptotically Minkowski spacetimes