Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Energy-momentum tesor

  1. Aug 16, 2005 #1

    samalkhaiat

    User Avatar
    Science Advisor

    How can you go about and prove the following :
    The energy-momentum tensor for any classical field theory = -2 X the functional derivative of the action with respect to the metric tensor.
     
  2. jcsd
  3. Aug 18, 2005 #2

    hellfire

    User Avatar
    Science Advisor

    Basically, if you have an action for matter interacting with gravity S = SG + SM and perform the functional derivative of S with respect to the metric tensor, you will get a first part corresponding to SG, which will be Einstein’s equations in vacuum, and a second part corresponding to SM, which will be the source of gravity. This is the covariant energy momentum tensor.
     
  4. Aug 19, 2005 #3

    samalkhaiat

    User Avatar
    Science Advisor

    You are right, this is how text books "define" the mater field E-M tensor in GR. This was not what I asked. I wanted a proof for the following;
    given any "free" matter field Lagrangian, show that the symmetric E-M tensor is equal to -2 X the functional derivative of the "free" matter action with respect to the metric tensor.(I am asking for proof with no reference to gravity). thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Energy-momentum tesor
Loading...