Beyond GRMHD: A Robust Numerical Scheme for Extended, Non-Ideal General Relativistic Multifluid Simulations

Abstract

The equations of general relativistic magnetohydrodynamics (GRMHD) have become the standard mathematical framework for modeling high-energy plasmas in curved spacetimes. However, the fragility of the primitive variable reconstruction operation in GRMHD, as well as the difficulties in maintaining strong hyperbolicity of the equations, sharply limit the applicability of the GRMHD model in scenarios involving large Lorentz factors and high magnetizations, such as around neutron stars. Non-ideal effects, such as electron inertia and Hall terms, are also neglected, and the absence of an explicitly evolved electric field precludes the self-consistent modeling of the strong poloidal fields found around spinning black holes, which are known to be crucial for jet formation. Here, we present a general relativistic multifluid model which strictly generalizes the GRMHD equations, consisting of an arbitrary number of relativistic fluid species interacting with a shared electromagnetic field via an explicit coupling of their source terms, thus allowing for the incorporation of non-ideal effects. We sketch how our model may be derived from general relativistic kinetics (via moments of the relativistic Boltzmann-Vlasov equation), as well as how GRMHD may be recovered in the single-fluid limit as the mobility of charge carriers goes to infinity. We present a numerical scheme for solving the general relativistic multifluid equations, and validate it against the analogous scheme for the GRMHD equations. Since the primitive variable reconstruction operation for our multifluid model is purely hydrodynamic, and therefore independent of the magnetic field, the resulting solver is highly robust, and able to simulate significantly larger Lorentz factors and higher magnetizations (across both black hole and neutron star spacetimes) than GRMHD without loss of either accuracy or stability.