On Lorentz spacetimes of constant curvature

TL;DR

This paper explores Lorentzian homogeneous spaces of constant curvature, focusing on the groups PSL(2,R) and its Lie algebra, and reviews recent findings on their quotient geometries by discrete groups.

Contribution

It provides a parallel description of these Lorentzian spaces and reviews recent advances in understanding their quotient geometries by discrete groups.

Findings

Descriptions of Lorentzian homogeneous spaces PSL(2,R) and its Lie algebra

Review of recent results on quotient geometries by discrete groups

Insights into the structure and properties of these Lorentzian spaces

Abstract

We describe in parallel the Lorentzian homogeneous spaces $G=\mathrm{PSL}(2,\mathbb{R})$ and $\mathfrak{g}=\mathfrak{psl}(2,\mathbb{R})$, and review some recent results relating the geometry of their quotients by discrete groups.