Stationary Spacetimes and Self-Adjointness in Klein-Gordon Theory
Mathematical Physics
2019-12-13 v1 General Relativity and Quantum Cosmology
Functional Analysis
math.MP
Abstract
We consider the problem of essential self-adjointness of the spatial part of the Klein-Gordon operator in stationary spacetimes. This operator is shown to be a Laplace-Beltrami type operator plus a potential. In globally hyperbolic spacetimes, essential selfadjointness is proven assuming smoothness of the metric components and semi-boundedness of the potential. This extends a recent result for static spacetimes to the stationary case. Furthermore, we generalize the results to certain non-globally hyperbolic spacetimes.
Keywords
Cite
@article{arxiv.1910.05322,
title = {Stationary Spacetimes and Self-Adjointness in Klein-Gordon Theory},
author = {Felix Finster and Albert Much and Robert Oeckl},
journal= {arXiv preprint arXiv:1910.05322},
year = {2019}
}
Comments
13 pages