Spinor calculus on five-dimensional spacetimes

Abstract

Penrose’s spinor calculus of four-dimensional Lorentzian geometry is extended to the case of five-dimensional Lorentzian geometry. Such fruitful ideas in Penrose’s spinor calculus as the spin covariant derivative, the curvature spinors, or the defi- nition of the spin coefficients on a spin frame can be carried over to the spinor calculus in five-dimensional Lorentzian geometry. The algebraic and differential properties of the curvature spinors are studied in detail, and as an application, we extend the well-known four-dimensional Newman–Penrose formalism to a five- dimensional spacetime.