From quantum to classical instability in relativistic stars

Abstract

It has been shown that gravitational fields produced by realistic classical-matter distributions can force quantum vacuum fluctuations of some nonminimally coupled free scalar fields to undergo a phase of exponential growth. The consequences of this unstable phase for the background spacetime have not been addressed so far due to known difficulties concerning backreaction in semiclassical gravity. It seems reasonable to believe, however, that the quantum fluctuations will ``classicalize'' when they become large enough, after which backreaction can be treated in the general-relativistic context. Here we investigate the emergence of a classical regime out of the quantum field evolution during the unstable phase. By studying the appearance of classical correlations and loss of quantum coherence, we show that by the time backreaction becomes important the system already behaves classically. Consequently, the gravity-induced instability leads naturally to initial conditions for the eventual classical description of the backreaction. Our results give support to previous analyses which treat classically the instability of scalar fields in the spacetime of relativistic stars, regardless of whether the instability is triggered by classical or quantum perturbations.