Kundt Three Dimensional Left Invariant Spacetimes

TL;DR

This paper characterizes Kundt spacetimes as Lorentz manifolds with specific geodesic vector fields, explores their local structure, and classifies all left invariant Kundt structures on three-dimensional unimodular Lie groups.

Contribution

It provides a detailed local description of Kundt spacetimes and offers a complete classification of left invariant Kundt structures on certain Lie groups.

Findings

Kundt spacetimes have a non-singular isotropic geodesic vector field with integrable orthogonal distribution.

The local structure of Kundt spacetimes is explicitly described.

All left invariant Kundt structures on three-dimensional simply connected unimodular Lie groups are classified.

Abstract

Kundt spacetimes are of great importance to General Relativity. We show that a Kundt spacetime is a Lorentz manifold with a non-singular isotropic geodesic vector field having its orthogonal distribution integrable and determining a totally geodesic foliation. We give the local structure of Kundt spacetimes and some properties of left invariant Kundt structures on Lie groups. Finally, we classify all left invariant Kundt structures on three dimensional simply connected unimodular Lie groups.