Cited by Lee Sonogan
Abstract by M. A. H. MacCallum
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.
Publication: Cornell University (Peer-Reviewed Journal)
Pub Date: 22 Apr, 2021 Doi: 10.1007/s10714-021-02829-9
Keywords: Semantic Spacetimes, Linear Isotropies, Spatial Rotations
https://arxiv.org/abs/2104.11297 (Plenty more sections and references int this research article)