181 research outputs found
Bianchi identities in higher dimensions
A higher dimensional frame formalism is developed in order to study
implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes
of the algebraic types III and N in arbitrary dimension . It follows that
the principal null congruence is geodesic and expands isotropically in two
dimensions and does not expand in spacelike dimensions or does not expand
at all. It is shown that the existence of such principal geodesic null
congruence in vacuum (together with an additional condition on twist) implies
an algebraically special spacetime. We also use the Myers-Perry metric as an
explicit example of a vacuum type D spacetime to show that principal geodesic
null congruences in vacuum type D spacetimes do not share this property.Comment: 25 pages, v3: Corrections to Appendix B as given in
Erratum-ibid.24:1691,2007 are now incorporated (A factor of 2 was missing in
certain Bianchi equations.
Electric and magnetic Weyl tensors in higher dimensions
Recent results on purely electric (PE) or magnetic (PM) spacetimes in n
dimensions are summarized. These include: Weyl types; diagonalizability;
conditions under which direct (or warped) products are PE/PM.Comment: 4 pages; short summary of (parts of) arXiv:1203.3563. Proceedings of
"Relativity and Gravitation - 100 Years after Einstein in Prague", Prague,
June 25-29, 2012 (http://ae100prg.mff.cuni.cz/
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