The proof showing that the energy-momentum tensor is symmetric uses the fact that $\partial_\nu T^{\mu\nu}=0$ due to translation symmetry, the definition of the conserved current and that $\partial_\nu J^{\mu\nu\rho}=0$ due to Lorentz symmetry:
\begin{equation} 0=\partial_\nu J^{\mu\nu\rho} = \partial_\nu (T^{\mu\nu}x^\rho - T^{\rho\nu}x^\mu) = x^\rho \partial_\nu T^{\mu\nu} + T^{\mu\nu} \partial_\nu x^\rho - x^\mu \partial_\nu T^{\rho\nu} - T^{\rho\nu}\partial_\nu x^\mu = T^{\mu\rho}-T^{\rho\mu} \end{equation}
My question is: is it possible to prove the energy-momentum tensor is symmetric only assuming Lorentz symmetry and not translation symmetry?
