# Stress-energy tensor definition

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?

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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.

Bill_K
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.

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.

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.

Thank you

Last edited:
Bill_K