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

The generalized general-relativisticmagnetohydrodynamic (generalized GRMHD) equations have been used to study specific relativistic-plasmas phenomena, such as relativistic magnetic reconnection or wave propagation modified by non-ideal MHD effects. However, the "Theta" term in the generalized Ohm law, which expresses the energy exchange between two fluids composing a plasma, has yet to be determined in these equations. In this paper, we determine the "Theta" term based on the generalized relativistic Ohm law itself. This provides closure of the generalized GRMHD equations, yielding a closed system of the equations of relativistic plasma. According to this system of equations, we reveal the characteristic scales of non-ideal MHD phenomena and clarify the applicable condition of the ideal GRMHD equations. We evaluate the characteristic scales of the non-ideal MHD phenomena in the M87* plasma using the Event Horizon Telescope observational data.