Talk:Frame fields in general relativity

Hi CH. Very nice article !

I haven't checked all the details of the calculations, but the article is very readable and good insights are obtained from the chosen examples. Just a quick query - is it worth doing a non-vacuum example ? I know, the article would become massive; perhaps this is too complicated, but if some valuable insight can be gained from a non-vacuum example, it may be worthy of consideration. --Mpatel 10:27, 30 July 2005 (UTC)

Hi, M--- glad you like the article! I already had the same idea, this is a work in progress... I decided a few days ago to create new articles "Observers in the Schwarzschild vacuum" and "Observers in the FRW dusts" to hold more extensive examples. I got lazy and failed to explain what I am doing in the talk pages, but my plans have (as often happens) rapidly gotten rather ambitious: some solutions (Schwarzschild, FRW, Kerr) are so important that they deserve extensive discussions of several types of observer (several frames) in several charts.

In the Schwarzschild vacuum, I currently plan to eventually discuss the following coordinate charts:

• Schwarzschild or static or "curvature",
• Eddington/Finklestein (ingoing/outgoing),
• Painleve (including infall from any rest at any given radius),
• Kruskal/Szekeres

and in each of these I plan to discuss the following frames:

• static observers,
• slowfall observers (accelerate radially outwards with thrust m/r^2),
• LeMaître observers (radially infalling from rest at spatial infinity, or more generally from any radius)

I also plan to discuss geodesics and strong lensing using static frame in some additional charts:

• polar spherical spatially isotropic to $E^{3}$,
• Costa chart, which is spatially isotropic to cylinder $R\times S^{2}$

I also plan to discuss Hagihara frame (observers in stable circular orbits) in static coordinates, including :a short derivation of the geodetic precession or de Sitter precession. And I plan to discuss the Weyl canonical chart for the Schwarzschild vacuum (in which it looks superficially like analogue of gravitational field outside a constant density Newtonian rod).

In FRW models (dust and perhaps radiation fluid), I plan to discuss comoving frame and an inertial frame moving with "constant velocity" wrt the comoving frame. This shows effects of moving w.r.t. "distant stars", and density and pressure behave as you would expect.

Eventually, I plan to discuss Kerr vacuum and its relatives (Kerr-Newman-NUT-de Sitter) using Boyer/Lindquist, Eddington, Doran (generalization of Painleve), Weyl/Lewis/Papapetrou canonical charts (for Ernst vacuum family) and Kerr/Schild charts. I plan to tie this in with forthcoming article on the fascinating Ernst vacuums, including the symmetry group of this family (all stationary axisymmetric vacuum solutions). I plan articles on colliding plane waves, and I plan to tie in Kerr and Schwarzschild articles with "Schwarzchild-generating", "Kerr-generating", "NUT-genrating" colliding plane wave models. I also plan to discuss Ehlers vacuum family (all cylindrically symmetric vacuums) and tie this in with Einstein/Rosen wave solutions, and thus with pp-waves and back to colliding plane waves and Ernst family. Also I plan to tie in the Gowdy vacuums, which are also part of this circle of ideas. Eventually I want to discuss some solution generating techniques and the physical significance of the symmetry groups, e.g. from the symmetry group of th e Weyl family we find that we can linearly superimpose a static line mass (locating on the axis of symmetry) in any Weyl vacuum. This is analogous to the possibility of linearly superimposing pp waves having the same wave vector field.

Before I get to this stuff, though, I need to write "electrovacuum solution" article and "Lambda-vacuum article" and "scalar field solution" article, meaning things like minimally coupled massless scalar field or conformally coupled massless scalar field. I am stymied by lack of good short standard names here, and open to suggestions for better names!---CH (talk) 02:14, 1 August 2005 (UTC)

Hi Chris. As for standard short names, the research literature may have some (I'm not aware of any standard short names for the above), but if not, then I can only suggest 'acronymising' the terms, e.g. conformally coupled massless scalar field could be acronymised to CCMSP. It's ugly, I know, but can't think of a better solution. ---Mpatel (talk) 10:28, August 14, 2005 (UTC)

We're on the same page, then, since I've been referring for years to "mcmsf" for minimally coupled massless scalar field" and "ccmsf", etc. Unfortunately, "massive" and "massless" both have the same initial! I am calling the article "Scalar field solution" and plan to eventually discuss curvature coupling and massless/massive alternatives in the text.

Here's someething weird: I am having difficulty seeing your (6.28 GMT today) revision of the page Talk:Vacuum solution (general relativity). I can see from "history" that you added a comment, but when I go to the page I seem to see the old version! ---CH (talk) 16:56, 14 August 2005 (UTC)

Yeah, don't worry about that; I started editing the talk page of the vacuum solution (GR) article, but then I deleted it as I realised you had already mentioned what I was going to suggest. I should remember to read the whole article before doing anything ! ---Mpatel (talk) 14:15, August 16, 2005 (UTC)

Terminology

Hi CH. Just a niggly point: I thought 'tetrad' meant a basis for the tangent space at some point. In the article, it's used synonymously with 'frame field'. I would prefer to use 'tetrad field' instead of 'tetrad' in the article. When restricting discussions at a particular point, 'tetrad' should be used. I think we're just using different terminology (and dare I say it, one of us - probably me - is perhaps a little loose in using the standard terminology for 'tetrad', if there is a standard). ---Mpatel (talk) 12:38, 12 October 2005 (UTC)

Good point, I agree that it makes sense to say "frame field" for frames covering some neighborhood (specified) the first time we mention one, and "frame" thereafter, and in general to always clarify the first time we use "frame" or "tetrad".---CH (talk) 02:09, 15 October 2005 (UTC)

Students beware

I created the original version of this article, which concerns a topic particularly dear to my heart, and I had been monitoring it for bad edits, but I am leaving the WP and am now abandoning this article to its fate.

Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive. I emphatically do not vouch for anything you might see in more recent versions, although I hope for the best.

Good luck in your search for information, regardless!---CH 23:32, 30 June 2006 (UTC)

Math typo?

should it not be fo that bends inwards not eo. The former is the Lemaitre inertial observer, the latter is the accelerating static non-inertial observer standing still in curved spacetime.

Please clarify and sign your posts. --Michael C. Price ^talk 05:47, 9 December 2009 (UTC)

Modernization needed

Looking at this article, and looking at the article Cartan formalism, it seems clear that some work is needed to align these articles, modernize notation, and build a bridge to the concept of a frame bundle and a spin connection. This particular article should probably be renamed to orthonormal tetrad formalism, because that seems to be the general intent of it. It would also do with an even simpler introduction, articulate the properties of tetrads more generally, and then also go a bit farther, to clarify coordinate-free notation, with tetrads as sections of a frame bundle, and the gauge invariance of tetrads (the so-called "displacement gauge invariance" portion of general relativistic invariance). Exhibiting this gauge invariance would be nice, as currently, the spin connection article isn't insightful, either physically or mathematically. The article on the Cartan formalism seems to deal with the generic n-dimensional case, and also the non-orthonormal case, and that's fine, except that there's some fair amount of overlap of subject matter. The article on the Cartan formalism tackles the generic (m,n)-dimensional case, again, overlapping in content. All three articles would benefit from a refresh... I have no clue why I'm bothering to say this, or who I expect to act on this. 67.198.37.16 (talk) 08:07, 21 April 2019 (UTC)

I also suggest merging the tetrad formalism article and this page. 193.82.242.39 (talk) 23:32, 17 August 2023 (UTC)

Hmm. The tetrad formalism is just a redirect to Cartan formalism. It deals with the general n-dimensional case, and never mentions general relativity. So, shouldn't merge. Also, both articles are already long. 67.198.37.16 (talk) 03:39, 11 November 2023 (UTC)

Lemaître observers

The section called Lemaître observers in this article does not appear to be correct. Eyeballing the frame fields given there, they just seem to be wrong, but I have not rigorously double-checked. 67.198.37.16 (talk) 03:39, 11 November 2023 (UTC)