KLEIN-GORDON SOLUTIONS ON NON-GLOBALLY HYPERBOLIC STANDARD STATIC SPACETIMES

We construct a class of solutions to the Cauchy problem of the Klein-Gordon equation on any standard static spacetime. Specifically, we have constructed solutions to the Cauchy problem based on any self-adjoint extension (satisfying a technical condition: "acceptability") of (some variant of) the Laplace-Beltrami operator defined on test functions in an L-2-space of the static hypersurface. The proof of the existence of this construction completes and extends work originally done by Wald. Further results include: the uniqueness of these solutions; their support properties; the construction of the space of solutions and the energy and symplectic form on this space; an analysis of certain symmetries on the space of solutions; and various examples of this method, including the construction of a non-bounded below acceptable self-adjoint extension generating the dynamics.