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Relativity energy-momentum tensor

  1. Nov 24, 2011 #1
    1. The problem statement, all variables and given/known data

    Arrive at the orthogonality relation [itex]{T^{\mu}}_{\alpha}{T^{\alpha}}_{\nu} = K{\delta^{\mu}}_{\nu}[/itex]
    and determine K.

    2. Relevant equations
    [itex] T_{ij}=T_ji} [/itex]


    3. The attempt at a solution
    [itex] {T^{\mu}}_{\alpha}{T^{\alpha}}_{\nu} = {T^{\mu}}_0{T^0}_{\nu}+ {T^{\mu}}_i{T^i}_{\nu}[/itex]
    I am not sure how to continue from here, in which direction I should go...
    Thanks!
     
    Last edited: Nov 24, 2011
  2. jcsd
  3. Nov 24, 2011 #2

    dextercioby

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    Is T appearing in the Einstein equations ? If so, use them.
     
  4. Nov 24, 2011 #3
    No, we haven't even studied yet Einstein's equations (the context is special-relativistic electrodynamics. T is the enrgy-momentum (stress) tensor)
     
  5. Nov 25, 2011 #4

    dextercioby

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    Aaaa, you should have said that. Ok, then you know how T looks like in terms of F. Then just express the contraction in the LHS in terms of F and regroup it so that you'll get a scalar times unit tensor.
     
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