Higher dimensional bivectors and classification of the Weyl operator
Original version
Coley, A and Hervik, S. (2010). Higher dimensional bivectors and classification of the Weyl operator. Classical and Quantum Gravity, 27(1) doi:10.1088/0264-9381/27/1/015002Abstract
We develop the bivector formalism in higher dimensional Lorentzian
spacetimes. We define the Weyl bivector operator in a manner consis-
tent 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.
Description
This is an author-created, un-copyedited version of an article accepted for publication in Classical and quantum gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at doi:10.1088/0264-9381/27/1/015002.