The conservation of momentum and energy in electromagnetism is usually written as $$ \partial_\nu T^{\mu \nu} + \eta^{\mu \rho} f_\rho = 0 $$ where $T^{\mu\nu}$ is the electromagnetic stress-energy tensor and $f_\rho$ is the Lorentz force.
However the conservation of momentum and energy in general relativity is stated as the divergence of the total stress-energy tensor being zero. So is there a symmetric tensor $T_\text{Lorentz}^{\mu\nu}$ which divergence is $\eta^{\mu \rho} f_\rho$, so that $\partial_\nu(T^{\mu\nu}+T_\text{Lorentz}^{\mu\nu})=0$ ?
$T_\text{Lorentz}^{\mu\nu}$ would measure the energy and momentum of charged particules.
