Kundt Three Dimensional Left Invariant Spacetimes

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.

arXiv comment15 pages

References in corpus (8)

• Spacetimes characterized by their scalar curvature invariants
• Kundt Spacetimes
• Generalizations of pp-wave spacetimes in higher dimensions
• Lorentzian spacetimes with constant curvature invariants in three dimensions
• Supersymmetry, holonomy and Kundt spacetimes
• Kundt spacetimes in the Einstein-Gauss-Bonnet theory
• Differential invariants of Kundt spacetimes
• Locally Homogeneous Kundt Triples and CSI Metrics

Cited by in corpus (5)

• Self-gravitating solutions in Yang-Mills-Chern-Simons theory coupled to 3D massive gravity
• Gravitational Waves from Thurston Geometries
• The completeness problem on the pseudo-homothetic Lie group
• Parallel spinors for ${\mathrm{G}}_2^{\ast }$ and isotropic structures
• On completeness of foliated structures, and null Killing fields