Quantum-only metrics in spherically symmetric gravity

Abstract

The Einstein action for the gravitational field has some properties which make of it, after quantization, a rare prototype of systems with quantum configurations that do not have a classical analogue. Assuming spherical symmetry in order to reduce the effective dimensionality, we have performed a Monte Carlo simulation of the path integral with transition probability e−β|S| . Although this choice does not allow to reproduce the full dynamics, it does lead us to find a large ensemble of metric configurations having action |S| ≪ ¯h by several magnitude orders. These vacuum fluctuations are strong deformations of the flat space metric (for which S = 0 exactly). They exhibit a periodic polarization in the scalar curvature R. In the simulation we fix a length scale L and divide it into N sub-intervals. The continuum limit is investigated by increasing N up to ∼ 106; the average squared action 〈S2 〉 is found to scale as 1/N2 and thermalization of the algorithm occurs at a very low temperature (classical limit). This is in qualitative agreement with analytical results previously obtained for theories with stabilized conformal factor in the asymptotic safety scenario.