Talk:Cartan–Karlhede algorithm

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Nice article, but I have a few criticisms:

:* The Lorentzian case is easier than the Riemannian case, in the sense that there ought to be fewer functionally independent quantities in the curvature and its derivatives. (See below.)

:* It should be mentioned that the isotropy groups in question are in fact the isotropy groups of the tetrad components of the curvature and its covariant derivatives.

:* It's unclear to me how the non-compactness of the Lorentz group makes the curvature normalization more difficult. The distinguishing feature of the Lorentz case is the Petrov classification, which always singles out certain classes of normalizations for the curvature. If anything, this is a big bonus over the Riemannian case.

:* The Karlhede (et al) work on Lorentzian spaces uses Cartan's method as the starting point, and then uses the Petrov scheme to simplify matters even further by giving sharper upper bounds on the required number of derivatives. This article suggests that what Karlhede did was somehow different from Cartan's work on Riemannian spaces from the outset. It wasn't. Karlhede's contribution seems to me to be an effective implementation of Cartan's otherwise unwieldy machinery.

Then again, mathematical physicists drink a different flavor of koolaid than I do, so take these criticisms with a grain of salt. Cheers, Silly rabbit 19:17, 21 June 2006 (UTC)

:Hi, Silly, the next section describes something which has been a long time coming and which has nothing to do with you! Sounds like you can improve the article without help from me, fortunately. Best ---CH 22:09, 30 June 2006 (UTC)

What do you mean here by Riemannian. Riemannian in mathematics refers to a positive-definite structure in the tangent spaces, which is not the physical case. In GR you need to use an indefinite structure instead, so the appropriate notion is pseudo-Riemannian- or Lorentzian- or (the best notion) Minkowski-structure. Mathematically there is a huge gap between these structures. — Preceding unsigned comment added by 130.133.134.62 (talk) 18:25, 8 June 2012 (UTC)