Semiclassical gravity with a conformally covariant field in globally hyperbolic spacetimes
2021
We show two results for semiclassical gravity in globally hyperbolic spacetimes. First, we prove the existence of exact solutions to semiclassical gravity with a massless, conformally coupled Klein-Gordon field in globally hyperbolic spacetimes. Second, we prove that semiclassical gravity in (generically non-static) conformally static, globally hyperbolic spacetimes with a massless, conformally coupled Klein-Gordon field is well posed, when viewed as a coupled theory for the dynamical conformal factor of the metric and the Klein-Gordon theory. Namely, it admits unique and stable solutions whenever constrained fourth-order initial data for the conformal factor and suitably defined Hadamard initial data for the Klein-Gordon state are provided on a spacelike Cauchy surface.
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