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Stress-energy tensor definition

  1. Mar 29, 2013 #1
    I have seen two definitions with oposite signs (for one of the pressure terms in the formula) all over the web and books. I suspect it is related to the chosen metric signature, but I found no references to that.




    General Relativity An Introduction for Physicists from M. P. HOBSON, G. P. EFSTATHIOU and A. N. LASENBY uses a negative sign.

    Wald uses a positive sign..

    And so on..

    What's happening?
  2. jcsd
  3. Mar 29, 2013 #2


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    I don't think the signature matters. Stephani uses a + sign like your first example. I always used this form so it looks as if H, E & L are in a minority.
  4. Mar 29, 2013 #3


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    The coefficient of P is a projection operator into the 3-space orthogonal to uμ. If you use ημν = (1, -1, -1, -1) it should be uμuν - ημν, while if you use ημν = (-1, 1, 1, 1) it should be uμuν + ημν.
  5. Mar 29, 2013 #4


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    I guess that sorts out the issue.
  6. Mar 29, 2013 #5
    Thanks Bill. So the metric matters then. In the end I was just using:


    where "s" is the sign corresponding to the time coordinate.

    Where do I find more about this?

    Thank you
    Last edited: Mar 29, 2013
  7. Mar 29, 2013 #6


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    I'm not sure what you're looking for, but there's an online treatment of relativistic fluid dynamics here that's rather complete.
  8. Mar 29, 2013 #7
    That's it. Thanks again
  9. Apr 4, 2013 #8
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