Non-lorentzian spacetimes

TL;DR

This paper reviews recent developments in non-Lorentzian geometry, focusing on the classification of kinematical Lie algebras, their associated Klein geometries, and Cartan geometries characterized by intrinsic torsion.

Contribution

It provides a comprehensive review of non-Lorentzian geometries, including classification and geometric modeling, with new insights into their intrinsic torsion properties.

Findings

Classification of kinematical Lie algebras

Characterization of associated Klein geometries

Description of Cartan geometries via intrinsic torsion

Abstract

I review some of my recent work on non-lorentzian geometry. I review the classification of kinematical Lie algebras and their associated Klein geometries. I then describe the Cartan geometries modelled on them and their characterisation in terms of their intrinsic torsion. (To appear in the special issue "Applications of transformation groups" to be published by the Journal of Differential Geometry and Applications.)