Lanczos Potential / Tensor  

In General > s.a. riemann tensor.
* Idea: A tensor Labc proposed as a potential for the Weyl curvature tensor; It plays the same role in gravity as the vector potential plays in electromagnetism; Under some conditions it has a superpotential.
$ Def: In spinor notation, the tensor such that the Weyl spinor can be expressed as

ΨABCD = 2 ∇(AA ' LBCD) A' .

* Conditions: The Weyl spinor has Lanczos potentials in all spacetimes; The Weyl tensor has Lanczos potentials in all four-dimensional spaces, irrespective of signature, but does not exist in more than 4D.
> Online resources: see Wikipedia page.

Dynamics > s.a. higher-order gravity [Lanczos Lagrangian].
* Riemann-Lanczos equations: A system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order Lanczos tensor potential field.
@ References: Dolan & Kim PRS(94) [wave equation]; Cartin gq/99 [and linearized general relativity], ht/03 [as spin-2 field, Born-Infeld type]; Dolan & Gerber JMP(08) [integrability of Riemann-Lanczos equations].

References > s.a. perturbations in general relativity; spin coefficients.
@ General: Lanczos RMP(62); Roberts MPLA(89), NCB(95)gq/99 [interpretation]; Dolan & Muratori JMP(98) [with Ernst potential].
@ Existence: Edgar & Höglund PRS(97)gq/96, GRG(00)gq/97 [in 4D only]; Andersson & Edgar CQG(01) [for Weyl spinor, superpotentials]; Edgar & Höglund GRG(02)gq [non-existence in n ≥ 7]; Edgar JMP(03)gq [conditions].
@ Specific spacetimes: Gaftoi et al NCB(98), Acevedo et al G&C(04) [Kerr metric]; O'Donnell NCB(04) [conformally flat]; Mena & Tod CQG(07)gq [perturbed FLRW spacetime, and gravitational entropy].


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