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How to show pt=-E

  1. Nov 27, 2017 #1
    1. The problem statement, all variables and given/known data
    It is not a homework but I'm interested in. How to show, very often used, ##p_t=-E##

    2. Relevant equations
    ##p^{\mu}p_{\mu}=-1##
    ##H=\sum{p_i \dot{q}^i}-L##
    ##2L=u^{\mu}u_{\mu}##
    ##p_{\mu}=g_{\mu\nu}\dot{q}^{\nu}##

    3. The attempt at a solution
    ##H=1/2(g^{\mu\nu}p_{\nu})=1/2(g^{\mu t}p_t^2+g^{\mu r}p_r^2+g^{\mu \theta}p_\theta^2+g^{\mu \phi}p_\phi^2)##. I suppose that ##H=E## and ##p_\theta=p_\phi=0## when ##r\rightarrow \infty##. But it is probably wrong way...there are squares.
    Can you advice please?
     
  2. jcsd
  3. Dec 2, 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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