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Ricci tensor for electromagnetic field

  1. Apr 25, 2012 #1
    Electromagnetic fields mostly have a stress-energy tensor in which the trace is zero. Is traceless stress energy tensor always implies Ricci scalar is zero? If yes how to prove that?
    Last edited: Apr 25, 2012
  2. jcsd
  3. Apr 25, 2012 #2
    Yes. Just contract the EFE's:

    [itex]g^{\mu \nu }R_{\mu \nu}-\frac{1}{2}g^{\mu \nu }g_{\mu \nu }R=\kappa g^{\mu \nu } T_{\mu \nu }[/itex]

    [itex]R^\mu_{~\mu}-\frac{1}{2}\delta^{\mu}_{~\mu} R=\kappa T^{\mu}_{~\mu}[/itex]

    [itex]R=- \kappa T^{\mu}_{~\mu}[/itex]

    EDIT: I probably should have said yes, assuming no cosmological constant.
    Last edited: Apr 25, 2012
  4. Apr 25, 2012 #3
    Ok. Thanks. What is the physical meaning of traceless Ricci scalar or stress energy tensor? Why would the electromagnetic field have a traceless stress energy tensor?
  5. Apr 26, 2012 #4
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