GR as a gauge theory

  • #51
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There is no such thing as an a-posterior assumption. If something follows from you assumptions it is a consequence not an assumption.
lol, can't you recognize a joke?
 
  • #52
PAllen
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Here is an interesting discussion about analyticity in physics, one of the answers, by unknown even refers to GR (in this case it makes reference to the no-hair theorem that is also valid only for real analytic manifolds).

http://mathoverflow.net/questions/114555/does-physics-need-non-analytic-smooth-functions
General theorems of this type typically do required a number of technical assumptions to prove anything. Such theorems don't assume anything about the metric, thus they typically need smoothness assumptions to constrain the problem enough to accomplish the proof.

Again, in the case of uniquness of KS geometry, such additional assumption is not needed because the existence and vanishing of the Einstein tensor everywhere is already requiring a sufficient degree of smoothness.
 
  • #53
3,507
26
General theorems of this type typically do required a number of technical assumptions to prove anything. Such theorems don't assume anything about the metric, thus they typically need smoothness assumptions to constrain the problem enough to accomplish the proof.

Again, in the case of uniquness of KS geometry, such additional assumption is not needed because the existence and vanishing of the Einstein tensor everywhere is already requiring a sufficient degree of smoothness.
You are again conflating smoothness and analyticity.
 
  • #54
PAllen
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I must issue a correction here. I've read too many mathematically sloppy treatments of Birkhoff. It turns out, that as strong as it is, you really do need additional assumptions to arrive uniquely at the KS geometry. Here is a reference discussing these issues:

http://arxiv.org/abs/0910.5194
 
  • #55
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I must issue a correction here. I've read too many mathematically sloppy treatments of Birkhoff. It turns out, that as strong as it is, you really do need additional assumptions to arrive uniquely at the KS geometry.
Finally, I was starting to suspect your account had been stolen by someone not very reasonable. ;-)
 

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