A very subtle thing is in Wiki I found the energy-momentum tensor in GR is automatically symmetric.
So whether the relativistic energy-momentum tensor is always symmetric? Whether this implies some relativistic constrain?
So whether this is just some coincidence?
$T^{i0}$ energy flux , $T^{0i}$ momentum density. The Symmetry follows from the fact that energy and momentum are the same thing rewieved in different reference frames. If energy is flowing in the system , we must have momentum as well. Energy flux is thus equivalent to momentum density. This tensor is symmetric in general theory of relativity.
