A new class of semiclassical gravity solutions, gravitational quantum stealths and regular Cauchy horizons

We consider semiclassical gravity with a Klein-Gordon field with mass $m^2 \geq 0$ and curvature coupling $\xi = 1/2$. We identify a special class of Hadamard two-point functions for which the semiclassical system is quasi-linear hyperbolic and, within this class, provide the first well-posedness result for semiclassical gravity without spacetime symmetries. These two-point functions yield stress-energy expectation values proportional to the spacetime metric (modulo ambiguities). If the proportionality constant vanishes, one has a quantum version of gravitational `stealth' configurations. We discuss that some of these solutions have regular Cauchy horizons in the light of strong cosmic censorship.