# Does metric signature affect the stress energy tensor?

If one were to derive the stress-energy tensor for a metric with $(+,-,-,-)$ signature would it be different from the stress-energy tensor derived from the same metric but with $(-,+,+,+)$ signature?

• It doesn't make any real difference. – Mozibur Ullah Mar 5 '20 at 14:01
• I'm voting to close this question as off-topic because the re-edited answer is not really about physics ... – Mozibur Ullah Mar 5 '20 at 14:04

The sign convention for the stress-energy-momentum (SEM) tensor $$T^{\mu\nu}$$ is usually chosen such that the energy density $$T^{00}$$ is positive.
$$\tag{1} T^{\mu\nu}~:=~\pm \frac{2}{\sqrt{|g|}}\frac{\delta S}{\delta g_{\mu\nu}}, \qquad T_{\mu\nu}~:=~\mp \frac{2}{\sqrt{|g|}}\frac{\delta S}{\delta g^{\mu\nu}},$$ for Minkowski sign convention $$(\mp,\pm,\pm,\pm)$$, respectively.