Plasma flow in force-free magnetospheres: two-fluid model near pulsars and black holes

Force-free electrodynamics (FFE) governs the evolution of EM fields filled with plasma in the regime where the stress-energy tensor of the plasma is negligible compared to that of the electromagnetic (EM) field. A key advantage of FFE is that FFE equations only involve the EM degrees of freedom, without requiring any knowledge of the plasma dynamics. This advantage, however, can become a limitation when our focus is on understanding the motion of the plasma: the plasma behavior cannot be determined within the FFE framework. In this talk, we address this limitation by reintroducing plasma dynamics in the force-free system using the two-fluid model. We derive the general perturbative method and show how plasma is painted on a force-free solution as a function of boundary conditions that encode the information about the amount and energy of the plasma produced in gap regions where FFE is violated. Our method reveals that, in the force-free limit, plasma motion is completely described on the 1+1 dimensional field sheet experienced by the particles stuck to the magnetic field lines. We apply this method to the pulsars and black holes with the monopolar field and produce fully analytical models that capture the key features of the problem.