Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Geodesic Equation

  1. Aug 16, 2015 #1
    As the geodesic equation in a form of
    ed2e808ce2b6aa1859eb947f21f23ec0.png
    is quite familiar for me. But I still cannot derive it in terms of time coordinate parameter;
    a82eae864b04bc27b468fc0becfabe9d.png
    I can't get the second term on the right hand side
    what I can get is
    ½{d[lngαβ(dxα/dt)(dxβ/dt)]/dt}dxμ/dt

    How can I obtain that term?
     
  2. jcsd
  3. Aug 16, 2015 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    I suggest you do not work in terms of the metric. The equation follows directly from the variable substitution to parameterise the curve with ##t## instead of ##s## and looking at how the geodesic equation transforms under this change. Keep in mind that
    $$
    \frac{d^2 t}{ds^2} = - \Gamma^0_{\alpha\beta} \dot x^\alpha \dot x^\beta .
    $$
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Geodesic Equation
  1. Geodesics equations (Replies: 3)

  2. Geodesic equation (Replies: 2)

  3. The geodesic equation (Replies: 5)

Loading...