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The generalized general-relativisticmagnetohydrodynamic (generalized GRMHD)equations have been used to study specific relativistic-plasmas phenomena, suchas relativistic magnetic reconnection or wave propagation modified by non-idealMHD effects. However, the "Theta" term in the generalized Ohm law, whichexpresses the energy exchange between two fluids composing a plasma, has yet tobe determined in these equations. In this paper, we determine the "Theta" termbased on the generalized relativistic Ohm law itself. This provides closure ofthe generalized GRMHD equations, yielding a closed system of the equations ofrelativistic plasma. According to this system of equations, we reveal thecharacteristic scales of non-ideal MHD phenomena and clarify the applicablecondition of the ideal GRMHD equations. We evaluate the characteristic scalesof the non-ideal MHD phenomena in the M87* plasma using the Event HorizonTelescope observational data.

Generalized general-relativistic magnetohydrodynamic equations for plasmas of active galactic nuclei in the era of the Event Horizon Telescope