Talk:Gödel metric
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[edit] Reason for underconstruction flag
Planned improvements:
- alternative physical interpretations:
- anti-stiff fluid
- dust plus Lambda
- minimally coupled massless scalar field plus Lambda
- cylindrical chart (see Hawking & Ellis)
- frame describing physical experience of particles whose world lines are closed timelike curves
- at least one derivation
- even more bizarre quotient manifolds
- larger families including Gödel and some other "rotating cosmological models".
I'll need some time to work this out since I know almost too much and might need to play around to strike the right balance, and perhaps spread some of this material over two or more articles.
Right now part of the discussion of physical properties only makes sense in another chart; I plan to fix this later today.---CH (talk) 22:32, 5 September 2005 (UTC)
[edit] Reason for removing underconstruction flag...
... without finishing the job. My recent work in preparing this article was prompted by my recent rediscovery of this solution in yet another chart (I have rediscovered the Gödel lambdadust a half dozen times in different coordinate charts), which is certainly simpler than others I've seen, but unforunately turned out to be rather misleading in terms of physical interpretation. In the course of sorting that out (never an easy task), I rediscovered a somewhat silly but also rather serious error which I noticed years ago (and had forgotten about) in the otherwise lovely figure in Hawking and Ellis (see note in the citation). My derivation of the claims made in the article has the advantage of being correct, but currently is too long and complicated to be included in the encyclopedia. Also, as often happens, preparing good figures (showing the appearance of the light cones) turned out to be a frustrating exercise in wrestling with limitations of maple graphical routines, and I'm not happy with the appearance of what I've produced thus far.
So I decided to declare this article as finished as anything ever is around here.---CH (talk) 06:56, 9 September 2005 (UTC)
[edit] Second revision
Decided I could compromise and introduce a cylindrical chart and some figures. Yes, the figures need to be cropped, and the first one is far too "dark" due to vagaries of Maple. When I get a chance I'll try to improve them.
[edit] Absolute future
I've redirected this link to light cone, which also needs a lot of work. ---Mpatel (talk) 11:54, September 10, 2005 (UTC)
- Well, my point is that these are two very different concepts (light cone at an event, at the level of a tangent space, versus absolute future, a certain region of the spacetime), and they deserve seperate (but linked) articles which are very well written.---22:09, 10 September 2005 (UTC)
[edit] Figures
OK, I've uploaded a much improved version of the previously substandard figure. I am considering trying to create an animated gif to more clearly illustrated what I am trying to explain about the frame which appears static in this chart (but which is really spinning!) versus the frame which appears to be spinning in this chart (but is really gyrostabilized), since this really a ubiquitious phenomenon whenever rotation is present, yet very few students seem to realize how this affects the interpretation of things like optical scalars and vorticity vectors (for null and timelike congruences respectively).
Eventually, it would be nice to have an interactive figure allowing user to drag a light cone around using his mouse, and watch its apparent shape change. This would be created by us using a tool like Maple as a set of images, with a very simple program choosing the appropriate image based on where the mouse cursor is located. Since (as in this example) some parameters might be inessential, this could save space. The only innovation would be a modest interactive capability in the Wiki software.
- Hmm... I've been trying off and on this afternoon to add another figure. Very strange: I can access the image page and verify that the image was uploaded, and when I "edit preview" the section on appearance of light cones, I can see the new image, but when I try to view the article itself, I cannot see it, and the edit history of the article fails to show further edits. I realize that Wikipedia physically exists on multiple servers, and that in particular the database server might fail to fully reflect edits, but this certainly seems stranger than anything I've seen thus far.
- Well, I discovered recently that it is possible to have an edit conflict with yourself (as a single logged in user), which certainly should not happen!
[edit] Students beware
I extensively rewrote the Sept 2005 original version of this article and 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. I hope for the best, but caution that this article is likely to attract future edits promoting personal points of view regarding so-called Mach principles, which is a perennially controversial topic in gravitation physics. Unfortunately, in the past, some WP editors have attempted to portray idiosyncratic personal views as if they belong to the canon of established mainstream scientific belief, which is unlikely to be accurate.
Good luck to all students in your search for information, regardless!---CH 00:40, 1 July 2006 (UTC)
