Spacetimes with continuous linear isotropies III: null rotations
General Relativity and Quantum Cosmology
2021-11-03 v1
Abstract
It is shown that in many cases local null rotation invariance of the curvature and its first derivatives is sufficient to ensure there is an isometry group G with dimension at least 3 acting on (a neighbourhood of) the spacetime and containing a null rotation isotropy. Invariance of the second derivatives is additionally required to ensure this conclusion in Petrov type N Einstein spacetimes, spacetimes containing "pure radiation" (a Ricci tensor of Segre type [(11,2)]), and conformally flat spacetimes with a Ricci tensor of Segre type [1(11,1)] (a "tachyon fluid").
Keywords
Cite
@article{arxiv.2106.01213,
title = {Spacetimes with continuous linear isotropies III: null rotations},
author = {M. A. H. MacCallum},
journal= {arXiv preprint arXiv:2106.01213},
year = {2021}
}
Comments
Formatted for submission to General Relativity and Gravitation. Parts I and II accepted there and in press