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

TL;DR

The paper demonstrates that, for a Klein-Gordon field with $m^2\ge0$ and $\xi=1/2$, a special class of Hadamard two-point functions yields a quasi-linear hyperbolic, well-posed semiclassical gravity system without symmetry assumptions. It shows that the quantum stress-energy tensor can be made proportional to the metric, enabling quantum stealth configurations when the proportionality vanishes, and provides a rigorous framework for reconstructing Hadamard two-point functions in a neighbourhood of a Cauchy surface. Through analytic initial data and Moretti's construction, the authors prove a local existence and uniqueness result for the paired system $(\mathscr{M},\omega_2)$ that solves the semiclassical Einstein equations with a Klein-Gordon field. They also present explicit examples and discuss implications for semiclassical cosmology and the possibility of regular Cauchy horizons, framing the results in the context of strong cosmic censorship and identifying open questions about positivity and the Hadamard property in broader settings.

Abstract

We consider semiclassical gravity with a Klein-Gordon field with mass $m^2 \geq 0$ and curvature coupling $ξ= 1/2$. 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.

Theorems & Definitions (1)

• Theorem 1