Spinor calculus on 5-dimensional spacetimes

Abstract

Penrose's spinor calculus of 4-dimensional Lorentzian geometry is extended to the case of 5-dimensional Lorentzian geometry. Such fruitful ideas in Penrose's spinor calculus as the spin covariant derivative, the curvature spinors or the definition of the spin coefficients on a spin frame can be carried over to the spinor calculus in 5-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 4-dimensional Newman-Penrose formalism to a 5-dimensional spacetime.

Convention mismatch and minor typos fixed. To appear in Journal of Mathematical Physics

References in corpus (4)

• Black Holes in Higher Dimensions
• xPerm: fast index canonicalization for tensor computer algebra
• Classification of the Weyl Tensor in Higher Dimensions and Applications
• On uniqueness of stationary vacuum black holes

Cited by in corpus (5)

• Refinements of the Weyl tensor classification in five dimensions
• Optical structures, algebraically special spacetimes, and the Goldberg-Sachs theorem in five dimensions
• Spinor description of $D=5$ massless low-spin gauge fields
• Mode Stability For Massless Scalars In Five-Dimensional Black Hole Backgrounds
• Killing Spinors and Related Symmetries in Six Dimensions