Semiclassical gravity with a conformally covariant field in globally hyperbolic spacetimes
Abstract
We prove that semiclassical gravity in conformally static, globally hyperbolic spacetimes with a massless, conformally coupled KleinGordon field is well posed, when viewed as a coupled theory for the dynamical conformal factor of the metric and the KleinGordon theory. Namely, it admits unique and stable solutions whenever constrained fourthorder initial data for the conformal factor and suitably defined Hadamard initial data for the KleinGordon state are provided on a spacelike Cauchy surface. As no spacetime symmetries are imposed on the conformal factor, the present result implies that, provided constrained initial data exists, there also exist exact solutions to the semiclassical gravity equations beyond the isotropic, homogeneous or static cases.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.01719
 Bibcode:
 2021arXiv211001719J
 Keywords:

 Mathematical Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 15 pages