Talk:Lanczos tensor

message: I think the dots need to be replaced with notation used elsewhere in gtr related pages.---CH  (talk) 00:19, 15 September 2005 (UTC)
thread_title: Notation

message: What to do, what to do... User:Markdroberts has not been heard from since Sept 23, and this article is inadequate as it stands (no clear motivation for either "Lanczos tensor", or how the Lanczos potential is related to the rank three tensor from Hawking & Ellis, etc). ---CH 09:20, 23 December 2005 (UTC)
thread_title: Fix or delete?

message: Recent improvements by User:Teply have helped immensely, but I think the article would look even better with a proper lead paragraph. It would be very informative to sum up the main significance in that lead before diving into the details. Rschwieb (talk) 13:47, 11 October 2012 (UTC)
replies: text: I see you went ahead and did that. That's what I had in mind... looks good! Rschwieb (talk) 13:02, 12 October 2012 (UTC)
thread_title:  Formatting the article so it isn't a giant stub 

message: I just found Nathalie Deruelle, John Madore's "On the quasi-linearity of the Einstein-'Gauss-Bonnet' gravity field equations" arXiv:gr-qc/0305004, which suggests Lanczos tensor originates in the article:
*Cornel Lanczos, "Elektromagnetismus als natürliche Eigenschaft der Riemannschen Geometrie." Zeitschrift für Physik A Hadrons and Nuclei 73 No 3-4 (1932), 147-168. DOI:10.1007/BF01351210
Unfortunately, I can't read German to verify the validity of Deruelle and Madore's claim. But I thought it ought to be mentioned...
A different version of the story is presented in P. O'Donnell and H. Pye "A Brief Historical Review of the Important Developments in Lanczos Potential Theory" eprint, which dates it back to 1938 as the discovery date, but it entered use in 1949. 
Just some preliminary research...-Pqnelson (talk) 02:34, 15 October 2012 (UTC)
replies: text: That arXiv link actually seems to be referring to the quadratic Lovelock tensor, which in 4D is just zero.  They also point out that this was already known in the 1921 Bach paper.  For a laugh, see equation 60 of .  See also the English language version of the 1932 paper.  The 1932 paper seems to be an important stepping stone, and the 1938 paper comes really close but just shy of the mark. Teply (talk) 07:28, 15 October 2012 (UTC)
thread_title:  Origin Incorrect? 

message: The "wave equation" could do with a little reformatting for readability, I think, such as by using the Cotton tensor instead its full expression. The equation looks a like an inhomogenous Klein–Gordon equation, making it a bit more complicated than a typical wave equation.  It might help if the trailing terms could be replaced by a single tensor contracted into the Lanczos tensor (the mass-squared term in the Klein–Gordon equation).  Would this make sense?  If we're going to make a statement that it is a wave equation (in the non-vacuum case), it should be made clear why this is so. — Quondum 13:58, 15 October 2012 (UTC)
replies: text: I have made the Cotton tensor more explicit as per my suggestion above. I do not have the references to be able to tackle the trickier matter of making it look more obviously like a wave equation. — Quondum 09:54, 17 October 2012 (UTC)
thread_title:  Wave equation 

message: AFAICT, the phrase "depends only on covariant derivative of the Ricci tensor and Ricci scalar" includes redundancy, since the covariant derivative of the Ricci scalar is an algebraic function of the covariant derivative of the Ricci tensor (non-mention of the metric tensor is already implicit). So we can simply drop "and Ricci scalar" without any inaccuracy. — Quondum 19:10, 18 October 2012 (UTC)
thread_title:  Unnecessary complexity of statement