The image from the wiki article on the stress energy tensor gives $T_{00}$ as $1/c^2$ times the energy density. I believe this is incorrect and that the $1/c^2$ factor should be dropped. Am I missing something?
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5Does this answer your question? Finding the correct units for the energy-momentum tensor? – pasaba por aqui Dec 23 '20 at 10:26
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The stress-energy tensor can be written with $T_{00}$ as an energy density or a mass density. The latter is of course just $E/c^2$ in accordance with Einstein's famous equation $E=mc^2$. Both forms are used and neither is more correct that the other.
In any case general relativists usually choose units where $c=1$ and the distinction disappears.
John Rennie
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Thank you John Rennie, but then the pressure diagonal (for instance) should be pressure divided by c squared shouldn’t it? If the wiki author puts in c’s and G’s then (s)he should be consistent no? – Polhode Feb 24 '18 at 16:46
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You are correct and Wikipedia is wrong. Energy density is $Nm/m^3 = N/m^2$ in SI units. Pressure is also $N/m^2$. Dividing $T^{00}$ by $c^2$ makes no sense.
Cuspy Code
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The other row that needs correction is the momentum density. If we drop the 1/(c squared) factor from T00 then we have to multiply the momentum density by a factor of c. The pressure and shear stress components remain unchanged. – Polhode Feb 24 '18 at 22:04
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@Polhode I agree. Looking at the talk page of the Wikipedia article, it seems one of the contributors insisted on working with a metric that has different units for different tensor components, which makes the article super-confusing. The Wikipedia article on the electromagnetic stress-energy tensor is much clearer in this regard. – Cuspy Code Feb 25 '18 at 15:02