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Transforming a metric

  1. Feb 23, 2016 #1

    PeroK

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    1. The problem statement, all variables and given/known data

    I have the metric ##ds^2 = -X^2dT^2 + dX^2##

    Find the coordinate transformation that reduces the metric to that of flat spacetime:

    ##ds^2 = -dt^2 + dx^2##

    2. Relevant equations


    3. The attempt at a solution

    I'm not sure there's a systematic way to solve this (or in general to show that a metric is just flat spacetime in a different coordinate system). And I've not been able to guess a suitable transformation.

    Any advice or hints on a technique or an inspired guess?
     
  2. jcsd
  3. Feb 23, 2016 #2

    Samy_A

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    Separation of variables (kind of)?
    ##t=Xf(T)##
    ##x=Xh(T)##
    Using the transformation rules for the metric tensor leads to the expected result, but I'm not sure it is the quickest (smartest) way to do it.
     
  4. Feb 23, 2016 #3

    PeroK

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    Yes, of course. I didn't think to try that way round. I was working with ##T = T(t,x)## etc. Many thanks.
     
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