A Noncommutative Deformation of General Relativity

TL;DR

This paper introduces a new framework for gravity using matrix-valued tensors, extending general relativity with noncommutative geometry and gauge symmetries, and recovers Einstein's theory in the classical limit.

Contribution

It presents a novel noncommutative deformation of general relativity with a matrix-valued tensor and associated gauge symmetry, expanding the theoretical landscape of gravitational models.

Findings

Constructed an invariant functional reducing to Einstein-Hilbert action

Introduced gauge symmetry for new degrees of freedom

Framework recovers classical general relativity in the commutative limit

Abstract

We develop a novel approach to gravity in which gravity is described by a matrix-valued symmetric two-tensor field and construct an invariant functional that reduces to the standard Einstein-Hilbert action in the commutative limit. We also introduce a gauge symmetry associated with the new degrees of freedom.