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

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.