Counting the number of Killing vectors in a 3D spacetime
General Relativity and Quantum Cosmology
2021-11-17 v2 High Energy Physics - Theory
Differential Geometry
Abstract
We devise an algorithm which allows one to count the number of Killing vectors for a Lorentzian manifold of dimension 3. Our algorithm relies on the principal traces of powers of the Ricci tensor and branches intricately according to the values of differential invariants arising from the compatibility conditions of the Killing equation. As illustrating examples, we classify the Lifshitz and pp-wave spacetimes into a hierarchy based on their level of symmetry. A complete classification of spacetimes admitting 4 Killing vectors is also presented.
Keywords
Cite
@article{arxiv.1902.07899,
title = {Counting the number of Killing vectors in a 3D spacetime},
author = {Masato Nozawa and Kentaro Tomoda},
journal= {arXiv preprint arXiv:1902.07899},
year = {2021}
}
Comments
53 pages, 17 figures; v2: published version