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DEC with E/M and scalar fields

  1. Nov 2, 2007 #1
    Hi,

    I'm trying to show that electromagnetism and scalar field theories satisfy the DEC. I know how to find [tex]T_{\mu\nu}[/tex] and all that and what I have to show ([tex]T_{\mu\nu} T^\nu_{\ \lambda} t^\mu t^\lambda\leq 0[/tex] and [tex]T_{\mu\nu} t^\mu t^\nu\geq 0[/tex] for timelike [tex]t^\mu[/tex]), but I'm having trouble getting started.

    Thanks!

    (Edit: Make that just the minimally coupled scalar field theory, [tex]T_{\mu\nu} = \nabla_\mu \phi \nabla_\nu \phi - \frac{1}{2}g_{\mu\nu}\nabla^\sigma \phi \nabla_\sigma \phi - g_{\mu\nu}V(\phi)[/tex] for some positive potential)
     
    Last edited: Nov 2, 2007
  2. jcsd
  3. Nov 2, 2007 #2

    Chris Hillman

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    This is a homework problem, correct? (There is a special PF forum with special rules for these.)
     
  4. Nov 2, 2007 #3
    It's a former homework problem, I wasn't satisfied with my solution.
     
  5. Nov 2, 2007 #4

    robphy

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    So, what did you try in your attempt?
     
  6. Nov 2, 2007 #5

    pervect

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    That applies to undergraduate homework problems. Graduate homework problems can optionally be posted to the main forums. But it is still required to show one's work.

    To quote the relevant section from the rules (I should add for people new to the forum that one can click on the link named "rules" to see the current PF rules)

     
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