Gravity and the Structure of Noncommutative Algebras

TL;DR

This paper explores how noncommutative geometry can be used to model gravitational fields, proposing a correspondence between algebraic perturbations and gravitational perturbations, with evidence provided for Minkowski space-time.

Contribution

It introduces a framework linking noncommutative algebra perturbations to gravitational field variations, specifically demonstrating this in Minkowski space-time.

Findings

Perturbations in noncommutative algebra correspond to linear gravitational perturbations.

The approach provides a new way to understand gravity through algebraic structures.

Evidence supports the conjecture in the context of Minkowski space-time.

Abstract

A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define the algebra there corresponds a linear perturbation of the gravitational field. This is shown to be true in the case of a perturbation of Minkowski space-time.