Quantum Space-time and Classical Gravity

TL;DR

This paper explores a method for defining differential calculi over noncommutative algebras, demonstrating that a natural calculus leads to flat Minkowski space-time, while perturbations introduce gravitational fields.

Contribution

It introduces a natural differential calculus on noncommutative space-time that inherently results in flat Minkowski space, and shows how perturbations can generate gravity.

Findings

Natural calculus yields flat Minkowski space-time.

Perturbations of the calculus produce non-trivial gravitational fields.

The approach links noncommutative geometry with classical gravity.

Abstract

A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a natural differential calculus using which the space-time is necessarily flat Minkowski space-time. Perturbations of this calculus are shown to give rise to non-trivial gravitational fields.