Essential self-adjointness for the Klein-Gordon type operators on asymptotically static spacetime

Abstract

Let $X=\mathbb{R}\times M$ be the spacetime, where $M$ is a closed manifold equipped with a Riemannian metric $g$, and we consider a symmetric Klein-Gordon type operator $P$ on $X$, which is asymptotically converges to ${\partial }_t^2-{△}_g$ as $|t|\to \infty$, where ${△}_g$ is the Laplace-Beltrami operator on $M$. We prove the essential self-adjointness of $P$ on $C_0^{\infty }(X)$. The idea of the proof is closely related to a recent paper by the authors on the essential self-adjointness for Klein-Gordon operators on asymptotically flat spaces.

References in corpus (5)

• Feynman Propagators on Static Spacetimes
• Hadamard property of the in and out states for Klein-Gordon fields on asymptotically static spacetimes
• An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime
• Pseudodifferential Weyl Calculus on (Pseudo-)Riemannian Manifolds
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Cited by in corpus (3)

• A remark on the essential self-adjointness for Klein-Gordon type operators
• Spatially flat FLRW spacetimes with a Big Bang from matrix geometry
• Propagators in curved spacetimes from operator theory