$$\begin{equation}(adsbygoogle = window.adsbygoogle || []).push({});

0 = ({\rho}_m + P_m)u^{m}_iu^{m}_j + \frac{4}{3}{\rho}_ru^{r}_iu^{r}_j

\end{equation}$$

where i,j = 1,2,3 and different. That is the off-diagonal elements of the tresstensor for matter fluid and radiation fluid.

The energy conditions imply that

##\rho_m + p_m > 0## and ##\rho_r > 0##

This implies that

$$\begin{equation}

u^{m}_1=u^{m}_2=u^{m}_3=u^{r}_1=u^{r}_2=u^{r}_3=0

\end{equation}$$

But how do one conclude the last equality?

edit: Tried to write in latex-code, but it doesn't seem to work (I don't know how to do).

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# Comoving fluids - radiation and matter

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