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arXiv · 1910.05322

Stationary Spacetimes and Self-Adjointness in Klein-Gordon Theory

Felix Finster·Albert Much·Robert Oeckl
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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.

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Felix Finster, Albert Much, Robert Oeckl. 2019-10-11. Stationary Spacetimes and Self-Adjointness in Klein-Gordon Theory. https://doi.org/10.1016/j.geomphys.2019.103561

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