Preprint Article Version 1 This version is not peer-reviewed

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.

Journal reference: Symmetry 2019, 11, 1288
DOI: 10.3390/sym11101288

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''.

Subject Areas

general relativity; euclidean quantum gravity; path integral; lattice field theory; metropolis algorithm

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