As I understand it, the component $T_{00}$ of the stress-energy tensor contains the energy density (which equals the mass density), $T_{0i}$ are the impulse flows (intuitively speaking, the velocities), and $T_{ii}$ (the diagonals of the stress tensor) are the pressures in the respective directions.
In which of these components 'goes' the kinetic energy of the matter's heat?
On a microscopic level, heat is just motion, so I suppose it should be in $T_{0i}$.
However, if you look at the sun as one homogeneous body like in a Schwarzschild solution, I'm not sure where to put it.
- Is it just energy, so it's part of $T_{00}$? This would mean that $T_{00}$ does not equal the mass density.
- Or is it part of the pressure, thus going to $T_{ii}$?