Talk:Schwarzschild coordinates

message: Schwarzschild coordinates can be used for any static spherically symmetric spacetime.  The defining characteristic of these coordinates is the fact that the radial coordinate is related to the length around circles r=r_0 by the usual formula C = 2 \pi r.  Compare isotropic coordinates.
: If I'm not mistaken, the Schwarzschild geometry is the geometry of a spherically symmetric spacetime - see Birkhoff's theorem (relativity).  Thus, the statement that Schwarzschild coordinates can be used for any [static] spherically symmetric spacetime seems almost trivial to me.  However, the defining characteristic stuff seems like a good thing to add to the article.  Alfred Centauri 02:30, 25 Jun 2005 (UTC)
replies: text: When you will be done with these new articles? ;<)  Alfred Centauri 02:30, 25 Jun 2005 (UTC)
thread_title: Generalize discussion to all static spherically symmetric spacetimes

message: I have removed the tags and stub, since this is assuming a fairly complete form.  Still to be done: 
* add computation of Einstein tensor and wave equation via exterior calculus,
* write or expand stubby articles cited in this article
Hope everyone will be pleased with the revision.---CH  (talk) 16:01, 8 October 2005 (UTC)
replies: text: It's definitely a change.  I am not sure that it is not at too high a level now, but I am not about to roll it back.  At the least, you not only knew where you wanted to go but also how to get there.  Things like the radial coordinate not giving distances between the spheres are important, and yet although I was aware of it I had not gotten to the point of "fitting" it in.  For now, I will just study this article.  In many ways this article is now an example of how to do this kind of thing.  --EMS | Talk 17:03, 8 October 2005 (UTC)
thread_title: Major revision (8 Oct 2005)

message: I completely rewrote the Oct 2005 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'd like to hope for the best, but see my warning in Talk:Karl Schwarzschild#Students beware.
Good luck in your search for information, regardless!---CH 17:27, 1 July 2006 (UTC)
thread_title: Students beware

message: I would do away with the hats above indices. They indicate the coefficients are with respect to a moving frame (a not necessarily coordinate basis) but they are IMHO over-pedantic and simply look bad when typeset. Nobody of course uses them in actual calculations. Besides, if they are used with ijkl they must be used with 0123 as well for consistency. And this would be just plain unbearable!
In the "Generalizations" section the staticity assumption is removed. When this is done, two forms of the metric actually satisfy the given symmetry and signature constraints (the first one is listed in the article):
:ds^2 = -f(t,r)^2 \, dt^2 + g(t,r)^2 \, dr^2 + r^2 \, \left( d\theta^2 + \sin^2(\theta) \, d\phi^2 \right), 
and:
:ds^2 = +f(t,r)^2 \, dt^2 - g(t,r)^2 \, dr^2 + r^2 \, \left( d\theta^2 + \sin^2(\theta) \, d\phi^2 \right), 
They both must be put into the Einstein equation and then it turns out the first one is valid for \scriptstyle2m<r<\infty and the second one for 0<r<2m.
Finally, the first section says: "Birkhoff's theorem states that every isolated spherically symmetric vacuum or electrovacuum solution of the Einstein field equation is static" but this phrasing is true only in the exterior (Birkhoff says that f and g above are independent of t which is true both in the exterior and interior). In general one would say "Birkhoff's theorem states that every isolated spherically symmetric vacuum or electrovacuum solution of the Einstein field equation is a patch of the Schwarzschild metric", but this formulation would no longer be relevant to that section. Perhaps it's best to remove it and insert the corrected version somewhere else where it would be more a propos. JanBielawski 21:10, 13 August 2006 (UTC)
thread_title:  Hats and signatures 

message: In the opening paragraph, I think the following sentence is wrong:
:In the case of general relativity, Birkhoff's theorem states that every isolated spherically symmetric vacuum or electrovacuum solution of the Einstein field equation is static, but this is certainly not true for perfect fluids.
I think "static" should be "stationary".  Otherwise, the Kerr metric would violate Birkoff, right?  I haven't done any GR in some time, so I'll leave it up to someone more confident. Njerseyguy (talk) 21:48, 4 March 2010 (UTC)
replies: text: The Kerr metric is not spherically symmetric. It has circular symmetry about the axis of rotation, and invariance under time translation. JRSpriggs (talk) 22:09, 4 March 2010 (UTC)
replies: text: There's also confusion about static and stationary on the Birkhoff's theorem (relativity) page (see talk page there), it should be clarified and fixed. 67.198.37.16 (talk) 07:32, 21 February 2016 (UTC)
thread_title:  Static vs. Stationary