Recent content by avirab

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    Is curvature guaranteed if only one connection coefficient is 'large'

    Firstly, thanks, your point about the metric helped me spot the typo of f instead of f2. Also: re what you wrote: for ax <<1, a << 1/x, so x <<<<. But all this is irrelevant to my question: I am asking a subtle question, please try to understanding the issue even if I am not being...
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    Is curvature guaranteed if only one connection coefficient is 'large'

    Hi. I had written f in the metric instead of f2. See corrected version above. My points and question still stand. And re the connections: I am not talking of BC's at large r, or vanishing locally, I am talking of the classical limit.
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    Is curvature guaranteed if only one connection coefficient is 'large'

    da2 + db2 + dc2 is flat. f2(b)da2 + db2 + dc2 is not flat if f(b) has a non-zero second derivative. That's it. This form of metric is interesting for several reasons 1) because it is in some sense the simplest change one can make to a flat metric to make it curved. 2) This is basically the...
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    Is curvature guaranteed if only one connection coefficient is 'large'

    Thanks for the reply but it does not directly relate to my question : I wrote specifically about a flat metric with only ONE additional metric function, as in the example I gave, and in Einstein's entwurf metric. Calculating the Riemann tensor for such a metric (for the conditions stated) shows...
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    Is curvature guaranteed if only one connection coefficient is 'large'

    A (3-d or higher) metric which is flat except for one non-trivial metric function of a different coordinate - eg changing dx2 to f(y)dx2 in Euclidean or Minkowski metric [but not f(x)dx2] - is curved if f(y) has a non-zero second derivative; there is no way to make the f(y) 'disappear', ie to...
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