Semiclassical gravity with a conformally covariant field in globally hyperbolic spacetimes
Abstract
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 KleinGordon field in globally hyperbolic spacetimes. Second, we prove that semiclassical gravity in (generically nonstatic) 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.
 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:
 17 pages