Bianchi identities in higher dimensions

Details Bianchi identities in higher dimensions Bianchi identities in higher dimensions

2004-01-04

arxiv.org/abs/gr-qc/0401013v3

Class.Quant.Grav.21:2873-2898,2004; Erratum-ibid.24:1691,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, v3: Corrections to Appendix B as given in Erratum-ibid.24:1691,2007 are now incorporated (A factor of 2 was missing

Scientific paper

10.1088/0264-9381/21/12/007 10.1

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 $n$. It follows that the principal null congruence is geodesic and expands isotropically in two dimensions and does not expand in $n-4$ 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.

Affiliated with

Also associated with

No associations

Rating

Bianchi identities in higher dimensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bianchi identities in higher dimensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bianchi identities in higher dimensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-113404