English

Higher dimensional bivectors and classification of the Weyl operator

General Relativity and Quantum Cosmology 2010-01-06 v2

Abstract

We develop the bivector formalism in higher dimensional Lorentzian spacetimes. We define the Weyl bivector operator in a manner consistent with its boost-weight decomposition. We then algebraically classify the Weyl tensor, which gives rise to a refinement in dimensions higher than four of the usual alignment (boost-weight) classification, in terms of the irreducible representations of the spins. We are consequently able to define a number of new algebraically special cases. In particular, the classification in five dimensions is discussed in some detail. In addition, utilizing the (refined) algebraic classification, we are able to prove some interesting results when the Weyl tensor has (additional) symmetries.

Keywords

Cite

@article{arxiv.0909.1160,
  title  = {Higher dimensional bivectors and classification of the Weyl operator},
  author = {A Coley and S Hervik},
  journal= {arXiv preprint arXiv:0909.1160},
  year   = {2010}
}

Comments

25 pages; v2: some notation changed, typos fixed; CQG accepted

R2 v1 2026-06-21T13:43:16.770Z