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

TL;DR

This paper proves the essential self-adjointness of Klein-Gordon type operators on asymptotically static spacetimes, ensuring well-posedness of the associated quantum field equations in this geometric setting.

Contribution

It establishes essential self-adjointness for a class of Klein-Gordon operators on asymptotically static spacetimes, extending previous results to this geometric context.

Findings

Proves essential self-adjointness of Klein-Gordon operators on asymptotically static spacetimes.

Uses techniques related to asymptotically flat space analysis.

Ensures well-posedness of quantum field equations in this setting.

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 $\partial_t^2-\triangle_g$ as $|t|\to\infty$, where $\triangle_g$ 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.