Hello! This is my first post, and I was wondering if anyone could help my uncertainty about this problem.(adsbygoogle = window.adsbygoogle || []).push({});

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

given an observer's world line, X = 2T and the metric ds^{2}= -X^{2}dT^{2}+ dX^{2}, find the components of the observer's 4-velocity

2. Relevant equations

I'm using the equation that ds^{2}/dτ^{2}= u = e_{0}

3. The attempt at a solution

Taking our equation for ds^{2}and dividing it by dτ^{2}, I solve for dX^{2}/dτ^{2}= u^{2}, keeping in mind that this also equals -1, to get that dX^{2}/dτ^{2}= X^{2}dT^{2}/dτ^{2}- 1.

Is the correct way to think about it? And from the observers frame, is her 4-velocity u = ( X^{2}dT^{2}/dτ^{2}- 1, 0 , 0, 0 )?

Thanks so much for your help!

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# Homework Help: Finding the 4-velocity of a world line

Can you offer guidance or do you also need help?

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