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.

  • $\begingroup$ Doesn't this answer your question? en.wikipedia.org/wiki/… $\endgroup$
    – Kosm
    Jun 1, 2017 at 23:19
  • $\begingroup$ I think you basically answered your question in the last sentence. $\endgroup$
    – Javier
    Jun 2, 2017 at 0:07
  • $\begingroup$ @Javier Then I expect a formula of $T^{\mu\nu}_\text{Lorentz}$ as a function of the 4-current $J^\mu$, but I can't find it. $\endgroup$
    – V. Semeria
    Jun 2, 2017 at 7:38


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.