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];
Vishwakarma EPJC(21)-a2103 [physical meaning].
@ 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];
Roberts a1910 [Bianchi spacetime].
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 1 mar 2021