Spinor calculus on 5-dimensional spacetimes

Details Spinor calculus on 5-dimensional spacetimes Spinor calculus on 5-dimensional spacetimes

2009-05-18

arxiv.org/abs/0905.2846v2

J.Math.Phys.50:122504,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1063/1.3256124

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.

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