Ricci identities in higher dimensions
Abstract
We explore connections between geometrical properties of null congruences and the algebraic structure of the Weyl tensor in n>4 spacetime dimensions. First, we present the full set of Ricci identities on a suitable "null" frame, thus completing the extension of the Newman-Penrose formalism to higher dimensions. Then we specialize to geodetic null congruences and study specific consequences of the Sachs equations. These imply, for example, that Kundt spacetimes are of type II or more special (like for n=4) and that for odd n a twisting geodetic WAND must also be shearing (in contrast to the case n=4).
Cite
@article{arxiv.gr-qc/0701150,
title = {Ricci identities in higher dimensions},
author = {Marcello Ortaggio and Vojtech Pravda and Alena Pravdova},
journal= {arXiv preprint arXiv:gr-qc/0701150},
year = {2012}
}
Comments
8 pages. v2: typo corrected between Propositions 2 and 3. v3: typo in the last term in the first line of (11f) corrected, missing term on the r.h.s. of (11p) added, first sentence between Propositions 2 and 3 slightly changed