Talk:Deriving the Schwarzschild solution
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You have that T_ab = 0 => R_ab = 0. But, after checking the link to the field equations, it looks like T_ab = 0 => G_ab = 0 => R_ab = (R/2) g_ab. What am I missing? 03:08, 27 Apr 2005 (UTC)
- Have found the answer to my question. R_ab = (R/2) g_ab has only the solution R_ab = 0. May I suggest that this less than obvious detail be added to the main article? Alfred Centauri 13:09, 27 Apr 2005 (UTC).
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- Requested details added to main article. --- Mpatel 11:12, 11 Jun 2005 (UTC)
[edit] Merger
This article mostly overlaps Schwarzschild solution. The actual derivation of the standard form of the solution can in fact be explained in a paragrapha, so we propose to merge with that article. ---CH 22:36, 3 March 2006 (UTC)
- Hi CH. I agree that the derivation can be explained in a paragraph. In fact, I think there was a sketchy derivation in the main article about a year ago, but I realised that it would be better to have a separate article for a derivation. I created this article to specifically show readers how to actually derive an exact solution. I believe that this is very important and it conforms nicely with one of our objectives in the WikiProjectGTR, namely, to have articles representative of the work in GTR. Being such a standard procedure, I think it's worth showing an explicit derivation of such a historically important and still crucial solution in GR. I thought about doing the same for Kerr and Reissner-Nordstrom, but realised that this was unnecessary because this article gets the idea (of how to derive a metric) across with nice symmetry arguments. Thus, I would prefer that we not merge. MP (talk) 08:28, 5 March 2006 (UTC)
I've put a thread heading at Talk:Schwarzschild solution to cover the merge, as that's where the "mergeto" template points discussion. If either of you wants to put a brief statement there, that would be great. --Christopher Thomas 20:42, 27 August 2006 (UTC)
[edit] i need explanation
in section Simplifying the components it is written that Choosing one of these hypersurfaces (the one with radius r0, say), the metric components restricted to this hypersurface (which we denote by \tilde{g}_{22} and \tilde{g}_{33}) should be independent of θ and φ (again, by spherical symmetry). but \tilde{g}_{33} depends on θ.
- Hello there. I corrected my mistake. I meant to say 'unchanged under rotations of theta and phi' instead of independent of theta and phi' (see the assumption of spherical symmetry at the start of the article). Hope this clears up the confusion. MP (talk) 22:50, 26 May 2006 (UTC)
[edit] Static
There is a mistake (or at least sloppy phrasing) in the article when it states that according to Birkhoff's theorem we can dispose of the static assumption. This is false - in fact the Schwarzschild solution is not static inside the horizon. The correct statement of Birkhoff's theorem is that a spherically symmetric solution must be independent of the t-coordinate (and also asymptotically flat). Independence of t outside the horizon implies static (but it doesn't mean this inside as t is spacelike there). JanPB 00:04, 31 January 2007 (UTC)
