Talk:Birkhoff's theorem (relativity)

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[edit] Einstein/Maxwell field equations

Would anybody knowledgable replace this redlink in the article with something more relevant? This concept most likely exists, but surely not under this silly name. Thanks. Oleg Alexandrov (talk) 07:44, 6 January 2006 (UTC)

To the contrary, if you look over journals, the arxiv, and standard books like Griffiths Colliding Plane Waves, you'll find that Einstein-Maxwell solution is a standard term, although I'd probably agree not a very perspicacious one. It usually nmeans just a simultaneous solution to the sourcefree (curved spacetime) Maxwell EM field equation and Einstein gravitational field equation, with minimal curvature coupling, and with the only source of the gravitational field being the energy content of the source-free EM field. I prefer to call such solutions electrovacuums. From the name, Einstein-Maxwell could be taken to include things like a magnetized dust or a charged spherical shell, but in practice I've seen it applied almost exclusively to electrovacuum.
I won't be able to get to this for an unknown amount of time, but at least it is on my list. ---CH 23:22, 8 January 2006 (UTC)

[edit] Aymptotically Flatness

Does asymtotically flatness follow from staticity?

I think Birkhoff has proven that spherical symmetric vacuum solutions of Einsteins equations are static. So they of course correspond to the SS-solutions in that point, but SS solutions are asymtotically flat too. Where is the asymtotic flatness in Birkhoff's theorem or does it really follow from Birkhoffs assumptions as stated in the article?

193.170.62.194 (talk ยท contribs) (student access at University of Vienna)

Is this your question?: "is every spherically symmetric static vacuum solution a Schwarzschild vacuum solution, or must one add the additional hypothesis of asymptotic flatness?" ---CH 21:38, 6 June 2006 (UTC)

[edit] Students beware

I had been monitoring this article, 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.

Good luck in your seach for information, regardless!---CH 22:43, 30 June 2006 (UTC)

[edit] Something is wrong with the statement

The first paragraph says: Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be stationary and asymptotically flat. This is not correct as the solution is obviously not static inside the horizon. The statement should say Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be the Schwarzschild solution. Basically, it says that the solution when written in Schwarzschild's coordinates has coefficients independent of the t-coordinate. Outside the horizon this requirement together with the diagonal form of the metric do translate into "static" of course, but not inside. The t-independence inside means the metric is spatially homogeneous there. JanBielawski 19:07, 25 April 2007 (UTC)