Some Classical and Quantum Aspects of Gravitoelectromagnetism.

Giorgio Papini

doi:10.3390/e22101089

Abstract

It has been shown that, even in linear gravitation, the curvature of space-time can induce ground state degeneracy in quantum systems, break the continuum symmetry of the vacuum and give rise to condensation in a system of identical particles. Condensation takes the form of a temperature-dependent correlation over distances, of momenta oscillations about an average momentum, of vortical structures and of a positive gravitational susceptibility. In the interaction with quantum matter and below a certain range, gravity is carried by an antisymmetric, second order tensor that satisfies Maxwell-type equations. Some classical and quantum aspects of this type of “gravitoelectromagnetism” were investigated. Gravitational analogues of the laws of Curie and Bloch were found for a one-dimensional model. A critical temperature for a change in phase from unbound to isolated vortices can be calculated using an -model.

Highlights

It is known that, in certain approximations, Einstein equations can be written in the form of Maxwell equations
A rotationally-invariant quantum system acquires a privileged direction in the course of its evolution in curved space-time
This symmetry breaking takes the form of a space-time-dependent ground state (12) and of a topological singularity in (13) that leads to the phenomenon of condensation in an ensemble of like particles

Summary

Introduction

In certain approximations, Einstein equations can be written in the form of Maxwell equations. The gravitational field is represented by Kλ which is classical and contains a topological singularity generated by the curvature of space-time, while φ, which satisfies a quantum equation, is no longer rotational invariant. This transformation is discussed at length together with various aspects of the interaction of Kλ with matter. Where Γαμν are the Christoffel symbols, and by differentiating (28) we obtain the covariant derivative of Pμ α ν This result is independent of any choice of field equations for γμν.

The Gravitational WKB Problem

Vortices

A Minimal Lagrangian

The One-Dimensional Model

A Two-Dimensional Model

Summary and Conclusions