Stationary spacetimes and selfadjointness in KleinGordon theory
Abstract
We consider the problem of essential selfadjointness of the spatial part of the KleinGordon operator in stationary spacetimes. This operator is shown to be a LaplaceBeltrami type operator plus a potential. In globally hyperbolic spacetimes, essential selfadjointness is proven assuming smoothness of the metric components and semiboundedness of the potential. This extends a recent result for static spacetimes to the stationary case. Furthermore, we generalize the results to certain nonglobally hyperbolic spacetimes.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 February 2020
 DOI:
 10.1016/j.geomphys.2019.103561
 arXiv:
 arXiv:1910.05322
 Bibcode:
 2020JGP...14803561F
 Keywords:

 QFT;
 Globally hyperbolic spacetimes;
 Spectral Theory;
 Mathematical Physics;
 General Relativity and Quantum Cosmology;
 Mathematics  Functional Analysis
 EPrint:
 13 pages