Spacetimes with continuous linear isotropies I: spatial rotations
Abstract
The weakest known criterion for local rotational symmetry (LRS) in spacetimes of Petrov type D is due to Goode and Wainwright (1986). Here it is shown, using methods related to the Cartan-Karlhede procedure, to be equivalent to local spatial rotation invariance of the Riemann tensor and its first derivatives. Conformally flat spacetimes are similarly studied and it is shown that for almost all cases the same criterion ensures LRS. Only for conformally flat accelerated perfect fluids are three curvature derivatives required to ensure LRS, showing that Ellis's original condition for that case is necessary as well as sufficient.
Cite
@article{arxiv.2104.11297,
title = {Spacetimes with continuous linear isotropies I: spatial rotations},
author = {M. A. H. MacCallum},
journal= {arXiv preprint arXiv:2104.11297},
year = {2021}
}
Comments
Accepted for General Relativity and Gravitation. In press. Title was amended. This v2 is the 'author's accepted manuscript' version