Physical attributes of a mechanism behind matter field deformation in non-commutative gravity

TL;DR

This paper proposes a mechanism in non-commutative gravity that maps matter fields onto a non-commutative manifold, leading to a density field split into two distinct parts that can prevent singularity formation in high-density gravitational systems.

Contribution

It introduces a novel effective mechanism for matter field deformation in non-commutative gravity, relevant at high densities, which can halt gravitational singularities.

Findings

Deformation of density fields into on-cell and off-cell components.

Different thermodynamic properties of the two fields.

Upper bounds on density and curvature to prevent singularities.

Abstract

It is increasingly widely believed that at high levels of resolution spacetime geometry may be inherently non-commutative. In this work we introduce an effective mechanism that maps matter fields onto a non-commutative background manifold. The mechanism, which is relevant at high densities in strongly gravitating systems (black holes, early universe) deforms a density field into two distinct fields, one residing dominantly on the lattice tops (hereafter, on-cell) and the other residing dominantly in the inter-lattice regions (hereafter, off-cell). The two fields have different physical and themodynamic characterics which we describe, and some of which play a role in halting singularity formation resulting from gravitational collpse. The mechanism quantizes the fields, sets an upper bound on their density and off-sets curvature singularity formation.