Type: Article

Stationary spacetimes and self-adjointness in Klein–Gordon theory

Finster, F., Much, A., Oeckl, R.;

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 self-adjointness 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.