Towards a noncommutative version of Gravitation

TL;DR

This paper discusses the challenges and current research efforts in extending Alain Connes' noncommutative geometric model of gravity from Riemannian to Lorentzian signature, aiming for physically predictive theories.

Contribution

It analyzes the difficulties in generalizing noncommutative geometry-based gravity models from Riemannian to Lorentzian frameworks and reviews current approaches.

Findings

Identifies key obstacles in Lorentzian noncommutative geometry

Discusses potential strategies for model generalization

Highlights ongoing research efforts in the field

Abstract

Alain Connes' noncommutative theory led to an interesting model including both Standard Model of particle physics and Euclidean Gravity. Nevertheless, an hyperbolic version of the gravitational part would be necessary to make physical predictions, but it is still under research. We shall present the difficulties to generalize the model from Riemannian to Lorentzian Geometry and discuss key ideas and current attempts.