Stationary Spacetimes and Self-Adjointness in Klein-Gordon Theory
arXiv:1910.05322 · doi:10.1016/j.geomphys.2019.103561
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.
arXiv comment13 pages
References in corpus (8)
- Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes
- Dynamics in Non-Globally-Hyperbolic Static Spacetimes II: General Analysis of Prescriptions for Dynamics
- Global Hyperbolicity and Completeness
- An Integral Spectral Representation of the Propagator for the Wave Equation in the Kerr Geometry
- Dynamics in Stationary, Non-Globally Hyperbolic Spacetimes
- Global Hyperbolicity of Sliced Spaces
- Complex Structures for Klein-Gordon Theory on Globally Hyperbolic Spacetimes
- On sliced spaces: Global Hyperbolicity revisited