Gravity on Fuzzy Space-Time

TL;DR

This paper reviews recent developments in incorporating gravity into noncommutative space-time models, highlighting a special case where the noncommutative structure tightly constrains the gravitational field, which persists as a shadow in the classical limit.

Contribution

It identifies a specific noncommutative space-time model where the gravitational field is directly linked to the noncommutative structure, providing insights into quantum gravity.

Findings

Rigid relation between noncommutative structure and gravitational field

Gravitational effects as a shadow in the commutative limit

Special case of parallelizable noncommutative space-time

Abstract

A review is made of recent efforts to add a gravitational field to noncommutative models of space-time. Special emphasis is placed on the case which could be considered as the noncommutative analog of a parallelizable space-time. It is argued that, at least in this case, there is a rigid relation between the noncommutative structure of the space-time on the one hand and the nature of the gravitational field which remains as a `shadow' in the commutative limit on the other.