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Metrics with Zero and Almost-zero Einstein Action in Quantum Gravity
Version 1
: Received: 24 September 2019 / Approved: 25 September 2019 / Online: 25 September 2019 (08:56:59 CEST)
A peer-reviewed article of this Preprint also exists.
Modanese, G. Metrics with Zero and Almost-Zero Einstein Action in Quantum Gravity. Symmetry 2019, 11, 1288. Modanese, G. Metrics with Zero and Almost-Zero Einstein Action in Quantum Gravity. Symmetry 2019, 11, 1288.
Abstract
We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action SE « ħ. This is obtained through a Metropolis algorithm with weight exp(-β2SE2) and β » ħ-1. The squared action in the exponential allows to circumvene the problem of the non-positivity of SE. The discretized metrics obtained exhibit a spontaneous polarization in regions of positive and negative scalar curvature. We compare this ensemble with a class of continuous metrics previously found, which satisfy the condition SE=0 exactly, or in certain cases even the stronger condition R(x)=0 for any x. All these gravitational field configurations are of considerable interest in quantum gravity, because they represent possible vacuum fluctuations and are markedly different from Wheeler's ''spacetime foam''.
Keywords
general relativity; euclidean quantum gravity; path integral; lattice field theory; metropolis algorithm
Subject
Physical Sciences, Quantum Science and Technology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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