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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Finding the 4-velocity of a world line

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**