Higher dimensional bivectors and classification of the Weyl operator

Understand

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.