Cohomogeneity One Dynamics on Three Dimensional Minkowski Space

TL;DR

This paper classifies all Lie group actions of cohomogeneity one on three-dimensional Minkowski space, analyzing both proper and nonproper cases, and determines the causal nature of the resulting orbits.

Contribution

It provides a complete classification of cohomogeneity one Lie group actions on 3D Minkowski space, including orbit causal character analysis.

Findings

Classification of Lie groups acting by cohomogeneity one

Determination of causal characters of orbits

Analysis of proper and nonproper actions

Abstract

In this paper we give a classification of closed and connected Lie groups, up to conjugacy in $Iso({\mathbb{R}^3_1})$, acting by cohomogeneity one on the three dimensional Minkowski space $\mathbb{R}^3_1$ in both cases, proper and nonproper actions. Then we determine causal characters of the orbits.