2020/05/31 by Giovanni Modanese, G. Modanese · 1 citation
Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Circular symmetry #Curvature #Einstein #Gravitation #Monte Carlo method #Path integral formulation #Pulsars and Gravitational Waves Research #Quantum Chromodynamics and Particle Interactions #Scalar field #Thermalisation #gr-qc
paper · pdf · doi:10.3390/quantum2020021
published in Quantum Reports 2(2), 314-325 (Multidisciplinary Digital Publishing Institute) · 15 pages, 8 figures. Final journal version
openalex created_date 2020/05/21 · openalex publication_date 2020/06/18 · arxiv created 2020/06/21 · arxiv updated 2020/06/23 · openalex updated_date 2026/08/06
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 ∼ 10 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.