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.
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References
C. Lanczos, Rev. Mod. Phys. 34, 379 (1962)
H. Takeno, Tensor 15, 103 (1964)
P. O’Donnell, Electron. J. Theor. Phys. 7, 327 (2010)
E.T. Newman, R. Penrose, J. Math. Phys. 3, 566 (1962)
F. Bampi, G. Caviglia, Gen. Relativ. Gravit. 15, 375 (1983)
W.F. Maher, J.D. Zund, Nuovo Cimento A 57, 638 (1968)
P. O’Donnell, Introduction to 2-spinors in general relativity (World Scientific, Singapore, 2003) p. 95
W.K Atkins, W.R. Davis, Proceedings of the Cornelius Lanczos International Centenary Conference (SIAM, Philadelphia, 1994) pp. 506--508
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O’Donnell, P. On a new approach of deriving the Weyl-Lanczos equations giving rise to a physical interpretation of the Lagrange multiplier q . Eur. Phys. J. Plus 126, 87 (2011). https://doi.org/10.1140/epjp/i2011-11087-7
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DOI: https://doi.org/10.1140/epjp/i2011-11087-7