Talk:Stress–energy–momentum pseudotensor

message: Right now, Landau-Lifshitz pseudotensor is a redirect to this article.  But this article should be named Landau-Lifshitz pseudotensor (and expanded) since there are many others like Møller complex which probably need their own articles, since they have somewhat different motivations and uses.  An article called Stress-energy-momentum pseudotensors should be an umbrella article putting them in context and comparing them.
Just to add to the confusion, there are several variant spellings of "Lifshitz", although this is most common and should be preferred.---CH 22:50, 13 June 2006 (UTC)
replies: text: I hadn't realised there were so many stress-energy-momentum pseudotensors!  Yes, we need an umbrella page to list them.  You seem to be suggesting that "Møller complex" is one; "Einstein" and "Landau-Lifshitz" makes three.  Any more? --Michael C Price 11:03, 14 June 2006 (UTC)

text: I agree.  I have LL to hand and will add the Christoffel description soon.  I am not familar with the other pseudotensors you listed, so am probably not the best judge of what should go in the SEM pseudo article and what belongs in the LL pseudo article.--Michael C. Price talk 07:52, 13 April 2007 (UTC)
thread_title: Move

message: The more well-known stress energy pseudotensors are: Einstein [1], Papapetrou [2], Bergmann [3], Landau and Lifshitz [4], Møller [5], and Weinberg [6].Lantonov 06:45, 5 April 2007 (UTC)
replies: text: Note [7] is the same as [4], is the same as [6]. --Michael C. Price talk 08:28, 23 July 2007 (UTC)
thread_title:  Stress energy momentum complexes (pseudotensors) 

message: Just another nag before you continue: LLP is expressed by Christoffel symbols which are components of the Levi-Civita connection, not by the Levi-Civita connection in its coordinate-independent sense. --Lantonov 09:41, 18 April 2007 (UTC)
replies: text: Thanks, I'll look further into this: my understanding was that Christoffel symbols are defined in terms of the metric, whilst the LC connection is defined in terms of the covariant derivative.  In the absence of torsion tensor they become identical. The coordinate independent approach is an area I am currently weak on.--Michael C. Price talk 09:56, 18 April 2007 (UTC)
replies: text: I thought that the "modern" view was that the LC connection is the "true" underlying dynamical object, while the metric pops out as a side effect. That's the viewpoint that the use of fibre bundles suggests. (in the same way that A is the dynamical object in E&M, not E+B). 67.198.37.16 (talk) 01:21, 11 April 2016 (UTC)
thread_title:  Levi-Civita connection vs. Christoffel symbols 

message: I found the following in Babak-Grishchuk :
"In traditional field theories, one arrives, after some work, at the energy-momentum object
which is: 1) derivable from the Lagrangian in a regular prescribed way, 2) a tensor under
arbitrary coordinate transformations, 3) symmetric in its components, 4) conserved due to
the equations of motion obtained from the same Lagrangian, 5) free of the second (highest)
derivatives of the field variables, and 6) is unique up to trivial modifications not containing the field variables. There is nothing else, in addition to these 6 conditions, that we could demand from an acceptable energy-momentum object, both on physical and mathematical grounds." --Lantonov (talk) 06:27, 25 July 2008 (UTC)
thread_title: 6 conditions that an energy-momentum object must satisfy

message: I removed a paragraph from the intro that began "Some people object to this derivation on the grounds that pseudotensors are inappropriate objects in general relativity", because it doesn't make any sense:
*"... but the conservation law only requires the use of the 4-divergence of a pseudotensor which is, in this case, a tensor (which also vanishes)." Sure, but when one describes a vanishing divergence as a conservation law one is implying the existence of a conserved quantity. Anyone who objects to this construction is presumably objecting to the nature of the conserved quantity, not to the identically zero divergence.
*"Also, most pseudotensors are sections of jet bundles, which are perfectly valid objects in GR." When people complain about pseudotensors they're complaining about the breaking of general covariance. Nondynamical fields that explicitly break symmetries are of course valid mathematical objects; no one would argue otherwise, even the people who think that they're "inappropriate".
-- BenRG (talk) 05:42, 11 May 2010 (UTC)
replies: text: ...sure... presumably... Not good enough grounds for deletion.--Michael C. Price talk 05:52, 11 May 2010 (UTC)
replies: text: An object does not have to be a tensor in order to participate in generally covariant formulas. Most notably the Christoffel symbols are widely used in general relativity (indeed they are the gravitational force field) and they are not tensors. Also tensor densities play a big role in Maxwell's equations in curved spacetime. You just need to make sure that you know what the transformation law of the object is and that the transformations combine to give an invariant formula. JRSpriggs (talk) 10:59, 11 May 2010 (UTC)
thread_title:  Removed a paragraph 

message: If so, and if it is not too complicated, I think it would make a nice addition to the article.  Anyone have a source and/or the expertise for such a presentation?  —Quantling (talk | contribs) 19:07, 18 November 2010 (UTC)
replies: text: Being a pseudotensor I guess that it can't be derived by any variational technique.  Just a guess, though. --Michael C. Price talk 00:09, 19 November 2010 (UTC)
thread_title:  Can the Landau–Lifshitz pseudotensor be derived from the Lagrangian? 

message: Substituted at 07:09, 30 April 2016 (UTC)
thread_title: Assessment comment

message: I made a blog page with a detailed derivation of of all forms of LL pseudotensor. Anyone can take from it what he/she deems helpful and put it in the wiki article. I prefer to write it in the blog and not here because in the blog I am not restricted by the conventions and conditionals of Wikipedia. Lantonov (talk) 14:35, 7 April 2021 (UTC)
thread_title: Landau-Lifshitz pseudotensor blog

message: "The use of the Landau–Lifshitz pseudotensor, a stress–energy–momentum pseudotensor for combined matter (including photons and neutrinos) plus gravity" implies that the pseudotensor contains the energy of matter we well, which is not true.  It represents purely the gravitational or metric components.  cheers, Michael C. Price talk 18:29, 19 June 2023 (UTC)
replies: text: Agreed.  I made an edit.  Feel free to edit further.  —Quantling (talk | contribs) 22:36, 19 June 2023 (UTC)
thread_title:  LL should be just the gravitational energy 

message: I recognize this is a hard request, but much of this article could only be read by people with advanced degrees in mathematics. Those who have such, will already know a fair bit about it, so the article becomes a repository, rather than an explanation that invites the reader in. I have quite good mathematical skills, yet find this non-explanatory, and dense to the point of non-readable. Might someone provide an explanation of the meaning of the mathematics at each point, for someone who has perhaps a degree in physics, rather than a PhD level in the mathematics? Centroyd (talk) 10:55, 27 January 2024 (UTC)
replies: text: It would be useful to list some of the things that were hard to understand, which parts seemed dense or opaque. It is equally difficult for the experts to guess what it is that is confusing to the newcomer. 67.198.37.16 (talk) 14:18, 4 June 2024 (UTC)
thread_title:  Needs better explanation, supporting understanding of the mathematics. 

message: It would be useful to add a section on what is the relation to the well known energy flux carried by gravitational waves in the weak-field limit, how that is related to the LL expression. Are these identical only in some particular gauge? Bkocsis (talk) 19:07, 21 February 2024 (UTC)
replies: text: Yes, such a section would be useful. Weinberg's book does the weak-field limit, so he might present this. On the other hand, that book is old, maybe 50 years old now, and surely there are modern treatments. 67.198.37.16 (talk) 14:50, 4 June 2024 (UTC)
thread_title:  Weak field limit and relation to gravitational waves