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Solution to tensor differential equations

  1. May 30, 2010 #1
    hello all,

    I need two solutions to two different tensor diffeqs. I think I may have the solution to the sourceless equation, however I am in the dark about the one with the source.


    [tex] \left(\partial_{\gamma}\partial_{\alpha}+\imath k^{\beta}g_{\alpha\beta}\partial_{\gamma}\right) \phi=T_{\gamma\alpha}\phi [/tex]

    and

    [tex] \left(\partial_{\gamma}\partial_{\alpha}+\imath k^{\beta}g_{\alpha\beta}\partial_{\gamma}\right) \phi=0 [/tex].

    Any help would be appreciated.
     
  2. jcsd
  3. May 30, 2010 #2
    here is my solution for the source less equation, feel free to check it please.

    [tex] \phi^{\gamma\alpha}=Ae^{-\imath\left(\delta^{\gamma}_{\alpha}k_{\gamma}x^{\alpha}\right)}+Be^{-\imath\left(k_{\alpha}x^{\alpha}-k_{\gamma}x^{\gamma}\right)} [/tex]

    thanks.
     
  4. May 30, 2010 #3
    I also made the replacement [tex]k_{\beta}=k^{\alpha}g_{\alpha\beta} [/tex]
     
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