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Finding the 4-velocity of a world line

  1. Mar 4, 2012 #1
    Hello! This is my first post, and I was wondering if anyone could help my uncertainty about this problem.

    1. The problem statement, all variables and given/known data
    given an observer's world line, X = 2T and the metric ds2 = -X2dT2 + dX2, find the components of the observer's 4-velocity

    2. Relevant equations
    I'm using the equation that ds2/dτ2 = u = e0

    3. The attempt at a solution
    Taking our equation for ds2 and dividing it by dτ2, I solve for dX2/dτ2 = u2, keeping in mind that this also equals -1, to get that dX2/dτ2 = X2dT2/dτ2 - 1.

    Is the correct way to think about it? And from the observers frame, is her 4-velocity u = ( X2dT2/dτ2 - 1, 0 , 0, 0 )?

    Thanks so much for your help!
  2. jcsd
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