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General Relativity geodesics, killing vector, conserved quantities

  1. Jun 26, 2017 #1
    1. The problem statement, all variables and given/known data
    grquestion.png

    2. Relevant equations


    3. The attempt at a solution

    Let ##k^u## denote the KVF.

    We have that along a geodesic ##K=k^uV_u## is constant , where ##V^u ## is the tangent vector to some affinely parameterised geodesic.

    ##k^u=\delta^u_i## , ##V^u=(\dot{t},\vec{\dot{x}})## so we get

    ##K= g_{ii}\dot{x^i}=t^{p_i}\dot{x^i}=K## (1) is conserved.

    where dot denotes a derivative with respect to some affine parameter ##s##

    ATTEMPT AT QUESTION:

    I think this is a bad attempt but...

    The curves of constant ##x^i## are given by: ##\dot{x^i}=0## , so above if ##K=0## equation (1) is trivially satisfied.

    Any help appreciated, thanks .
     
  2. jcsd
  3. Jul 1, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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