Stress-energy tensor definition

  • Thread starter coleman123
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  • #1
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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.

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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?
 

Answers and Replies

  • #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.
 
  • #3
Bill_K
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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.
 
  • #4
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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.
I guess that sorts out the issue.
 
  • #5
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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.
Thanks Bill. So the metric matters then. In the end I was just using:

Tμν=(ρ+P/c2)uμuν-sPgμν

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

Where do I find more about this?

Thank you
 
Last edited:
  • #6
Bill_K
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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.
 
  • #7
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That's it. Thanks again
 

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