On a new approach of deriving the Weyl-Lanczos equations giving rise to a physical interpretation of the Lagrange multiplier q

Abstract

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 \(\ensuremath Q_{\alpha \beta}\) 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 \(\ensuremath H_{\alpha \beta \gamma }\) , \(\ensuremath Q_{\alpha \beta}\) and q when the Bianchi identities are invoked.