Beyond ideal magnetohydrodynamics: Resistive, reactive and relativistic plasmas

Abstract: We develop a new framework for the modelling of charged fluid dynamics in general relativity. The model, which builds on a recently developed variational multi-fluid model for dissipative fluids, accounts for relevant effects like the inertia of both charge currents and heat and, for mature systems, the decoupling of superfluid components. We discuss how the model compares to standard relativistic magnetohydronamics and consider the connection between the fluid dynamics, the microphysics and the underlying equation of state. As illustrations of the formalism, we consider three distinct two-fluid models describing i) an Ohm's law for resistive charged flows, ii) a relativistic heat equation, and iii) an equation representing the momentum of a decoupled superfluid component. As a more complex example, we also formulate a three-fluid model which demonstrates the thermo-electric effect. This framework allows us to model neutron stars (and related systems) at a hierarchy of increasingly complex levels, and should enable us to make progress on a range of exciting problems in astrophysics and cosmology.