https://doi.org/10.1140/epjp/i2011-11087-7
Regular Article
On a new approach of deriving the Weyl-Lanczos equations giving rise to a physical interpretation of the Lagrange multiplier q
Homerton College, University of Cambridge, Hills Road, CB2 8PH, Cambridge, UK
* e-mail: po242@cam.ac.uk
Received:
26
June
2011
Accepted:
14
September
2011
Published online:
22
September
2011
In this paper we incorporate Lanczos’ six differential gauge conditions and eight algebraic conditions to the tensor form of the Weyl-Lanczos equation and subsequently apply the null tetrad formalism to obtain the Weyl-Lanczos equation in spin coefficient form. This technique is then applied to the Ricci tensor. As a consequence, Lanczos’ Lagrange multiplier 
is found to be related to the Ricci tensor --and explicit forms are obtained involving spin coefficients and the eight complex Lanczos coefficients-- while the Lagrange multiplier q can be interpreted as the Ricci scalar. Furthermore, a relationship is established between 
, and q when the Bianchi identities are invoked.
© Società Italiana di Fisica and Springer, 2011
