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General Relativity

  1. Apr 18, 2010 #1
    I have two equations:

    [itex]\ddot{x}^\mu + \ddot{y}^\mu + \Gamma^\mu{}_{\nu \lambda} (x+y)(\dot{x}^\nu+\dot{y}^\nu)(\dot{x}^\lambda+\dot{y}^\lambda)=0[/itex]
    and
    [itex]\ddot{x}^\mu + \Gamma^\mu{}_{\nu\lambda}(x) \dot{x}^\nu \dot{x}^\lambda=0[/itex]

    apparently if i taylor expand the first equation to first order and then subtract the second equation i should get

    [itex]\ddot{y}^\mu + \frac{\partial \Gamma^\mu{}_{\nu\lambda}}{\partial x^\rho} \dot{x}^\nu \dot{x}^\lambda y^\rho = 0 [/itex]

    i cannot show this. how do we go about taylor expanding something like that?
     
  2. jcsd
  3. Apr 18, 2010 #2

    Fredrik

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    Same way you'd expand any other function [tex]f:\mathbb R^4\rightarrow \mathbb R[/tex].

    [tex]f(x+y)=f(x)+y^\rho f_{,\rho}(x)+\mathcal O(y^2)[/tex]
     
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