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Covariant derivative of stress-energy tensor

  1. Aug 9, 2011 #1
    hi, I understand that Tab,b=0 because the change in density equals the negative divergence, but why do the christoffel symbols vanish for Tab;b=0?
     
  2. jcsd
  3. Aug 9, 2011 #2

    Ben Niehoff

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    They don't. Why would you think that?

    I think your first equation came from flat space, because it is not true in curved space.
     
  4. Aug 9, 2011 #3

    WannabeNewton

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    [itex]\triangledown _{\mu }T^{\mu \nu } = 0[/itex] can be gotten from [itex]\triangledown_{\mu }G^{\mu \nu } = 0[/itex] which is a consequence of the second bianchi identity. You also know that [itex]T^{\mu \nu }, _{\mu } = 0[/itex] but what you can do is say that locally this is the same thing as [itex]T^{\mu \nu }; _{\mu } = 0[/itex] and if this is true for some coordinate system it will be true for all coordinate systems.
     
  5. Aug 9, 2011 #4
    thank you
     
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