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We construct a class of solutions to the Cauchy problem of the Klein-Gordonequation on any standard static spacetime. Specifically, we have constructedsolutions to the Cauchy problem based on any self-adjoint extension (satisfyinga technical condition: "acceptability") of (some variant of) theLaplace-Beltrami operator defined on test functions in an $L^2$-space of thestatic hypersurface. The proof of the existence of this construction completesand extends work originally done by Wald. Further results include theuniqueness of these solutions, their support properties, the construction ofthe space of solutions and the energy and symplectic form on this space, ananalysis of certain symmetries on the space of solutions and of variousexamples of this method, including the construction of a non-bounded belowacceptable self-adjoint extension generating the dynamics.

Klein-Gordon Solutions on Non-Globally Hyperbolic Standard Static Spacetimes