Essential Self-Adjointness of Klein-Gordon Type Operators on Asymptotically Static, Cauchy-Compact Spacetimes
Abstract
Let X=R×M be the spacetime, where M is a closed manifold equipped with a Riemannian metric q0, and we consider a symmetric Klein-Gordon type operator □g on X, which asymptotically converges to ∂t2-▵q0 as |t|→∞, where ▵q0 is the Laplace-Beltrami operator on M. We prove the essential self-adjointness of □g on C0∞(X). The idea of the proof is partly related to a recent paper by the authors on the essential self-adjointness for Klein-Gordon operators on asymptotically flat spaces.
- Publication:
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Communications in Mathematical Physics
- Pub Date:
- March 2023
- DOI:
- 10.1007/s00220-022-04543-2
- arXiv:
- arXiv:2203.00178
- Bibcode:
- 2023CMaPh.398.1153N
- Keywords:
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- Mathematical Physics;
- Mathematics - Analysis of PDEs;
- Mathematics - Functional Analysis
- E-Print:
- doi:10.1007/s00220-022-04543-2