Survey of Gravity in Non-Commutative Geometry

TL;DR

This paper surveys how Connes' Non-Commutative Geometry is applied to gravity, reviewing foundational theories, Euclidean models, and exploring challenges in extending to Lorentzian spacetime.

Contribution

It provides a comprehensive overview of non-commutative geometric approaches to gravity and discusses the difficulties in developing Lorentzian models.

Findings

Reviewed foundational aspects of non-commutative geometry in gravity

Analyzed Euclidean gravity models within the framework

Discussed challenges and existing attempts for Lorentzian generalization

Abstract

We present a survey of the application of Cones' Non-Commutative Geometry to gravitation. Bases of the theory and Euclidian gravity models are reviewed. Then we discuss the problem of a Lorentzian generalization of the theory and review existing attempts of solution.