Talk:Einstein-Hilbert action
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![S = \int \left[ k\, (R + \Lambda) + L_\mathrm{M} \right] \sqrt{-g} \, d^4x](../../../math/5/9/2/592768fe639db3f6cc29f19ad3c099bf.png)
The Einstein-Hilbert action as stated in the article is ![S[g]=k\int d^nx \sqrt{|\det(g)|} R](../../../math/e/6/b/e6b93c0019ad0b9eb96b234d74401b32.png)
. Unfortunately, there is no hint on the domain over which the integral is taken nor if g is varrying with x. Am I missing something or is the article missing something? 84.160.232.20 21:03, 10 September 2005 (UTC)
- The article is missing something, I guess. The integral is taken over (a neighborhood of) spacetime and g does vary. The volume element is just
for a four dimensional Lorentzian manifold, so this just says we integrate the Ricci scalar over spacetime. And in fact there is something to say about boundary terms.---CH (talk) 18:57, 21 October 2005 (UTC)
The integral is taken over the whole manifold, i.e. the whole space-time. Of course, the determinant of the metric g is varying with x (otherwise it should have been written in front of the integral) as it describes the shape of space-time, the same holds for the scalar curvature R. So for a flat Minkowski space-time, that's the shape of space-time without or very weak gravity, g does not depend on x, but a curved space-time has varying g. The usual approach to boundary terms in undergraduate texts is to simply not discuss them. The usual argument given, the article says the same, BTW, is that the variation is assumed to vanish at the boundary. Then the contribution of the boundary terms is multiplied by a zero. There is indeed more to be said about boundary terms, see for example AdS/CFT correspondence, but this goes far beyond a Wikipedia article, I think. The only thing I consider unfortunate is that the conventions seem to differ between different articles, for example the definition of the stress-energy tensor given there and in Einstein-Hilbert action.
[edit] Source for claim Einstein consulted Hilbert?
What is this claim that Einstein went to Hilbert to get the field eqiuations? Hilbert invited Einstein to Gottingen to give six 2-hour lectures in June-July 1915 on general relativity. This was prompted by Hilbert's reading Einstein/Grossmann "Outline" papers in 1914 where the idea of linking space-time curvature to gravity was introduced (Sauer 1999, Arch. Hist. Exact Sci, v53, p529-575). Hilbert was always seeking physicists for problems in theoreticfal physics (Hilbert had previously invivted Einstein to talk on the kinetic theory, which Einstein declined) - Einstein did not go to Hilbert for help. Sauer is a well–researched and foot-noted paper. E4mmacro 05:10, 10 March 2006 (UTC)
Didn't Hilbert derive the field actions from the action principle first? Einstein "derivation" of the field equations was more of a guess based on all the previous versions he had tried, not a derivation in any mathematical sense. When was it first called the Einstein-Hilbert action? E4mmacro 06:59, 26 March 2006 (UTC)
- Way too much ink has been spilled on this, but IMO standard biographies, recent history of science papers (by reputable researchers), and available primary sources make clear why the standard name is indeed appropriate. In any case, as far as WP is concerned, I think it suffices to agree that this is the standard name; this is not a forum for debating whether the standard name is somehow unfair to anyone. ---CH 01:22, 27 March 2006 (UTC)
Wasn't trying to change it or debate it. Just asking for confirmation that this is the standard name (and out of curiosity, when that standard name was first used). E4mmacro 09:42, 27 March 2006 (UTC)
