Quantum-only metrics in spherically symmetric gravity

G. Modanese

doi:10.3390/quantum2020021

paper

Quantum-only metrics in spherically symmetric gravity

arXiv:2005.07035 · doi:10.3390/quantum2020021

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 $∣ S ∣ ≪ ℏ$ 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 $\sim 1 0^{6}$ ; the average squared action $⟨ S^{2} ⟩$ is found to scale as $1/ N^{2}$ 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.

arXiv comment15 pages, 8 figures. Final journal version

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