On potentials for several classes of spinor and tensor fields in curved space-times

DOI10.1007/BF00758910zbMath0647.53056OpenAlexW2089939805MaRDI QIDQ1104577

Reinhard Illge

Publication date: 1988

Published in: General Relativity and Gravitation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00758910

zbMATH Keywords

vector potentialspinorsspace-timeMaxwell field tensorWeyl's conformal curvature tensor

Mathematics Subject Classification ID

General relativity (83C99) Spin and Spin({}^c) geometry (53C27) Applications of local differential geometry to the sciences (53B50)

Related Items

Letter to the editor: Nonexistence of the Lanczos potential for the Riemann tensor in higher dimensions ⋮ Electromagnetic interpretation of the massless spin-1 field equation in curved space-time ⋮ Curvature-free asymmetric metric connections and Lanczos potentials in Kerr–Schild spacetimes ⋮ Lanczos potential for the van Stockum space-time ⋮ On effective constraints for the Riemann–Lanczos system of equations ⋮ A solution of Weyl-Lanczos equations for arbitrary Petrov type D vacuum spacetimes ⋮ Lanczos potential for arbitrary Petrov type II spacetimes ⋮ A Lanczos potential in Kerr geometry ⋮ A potential for the radiative part of the Liénard-Wiechert field ⋮ A new Weyl-like tensor of geometric origin ⋮ Spin coefficients as Lanczos scalars: Underlying spinor relations ⋮ Relativistic potential of Weyl: a gateway to quantum physics in the presence of gravitation? ⋮ Local existence of symmetric spinor potentials for symmetric (3,1)-spinors in Einstein space-times ⋮ The Lanczos potential for Weyl-candidate tensors exists only in four dimensions ⋮ Some potentials for the curvature tensor on three-dimensional manifolds ⋮ Proofs of existence of local potentials for trace-free symmetric 2-forms using dimensionally dependent identities ⋮ AN ALGORITHM FOR THE ALGEBRAIC CLASSIFICATION OF THE SYMMETRIC (3,1)-SPINOR ⋮ A weighted de Rham operator acting on arbitrary tensor fields and their local potentials ⋮ A potential for the Lanczos spintensor in Kerr geometry ⋮ Massive fields of arbitrary spin in curved space-times ⋮ The non-existence of a Lanczos potential for the Weyl curvature tensor in dimensions \(n\geq 7\)

Cites Work

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• Is the Riemann tensor derivable from a tensor potential?
• Lanczos' splitting of the Riemann tensor
• Third-order tensor potentials for the Riemann and Weyl tensors
• The Splitting of the Riemann Tensor
• Selbstadjungierte huygenssche Differentialgleichungen zweiter Ordnung für nichtskalare Spintensorfelder