A new scheme for matching general relativistic ideal magnetohydrodynamics to its force-free limit

Abstract

We present a new computational method for smoothly matching general relativistic ideal magnetohydrodynamics (MHD) to its force-free limit. The method is based on a flux-conservative formalism for MHD and its force-free limit, and a vector potential formulation for the induction equation to maintain the zero divergence constraint for the magnetic field. The force-free formulation we adopt evolves the magnetic field and the Poynting vector, instead of the magnetic and electric fields. We show that our force-free code passes a robust suite of tests, performed both in 1D flat spacetime and in 3D black hole spacetimes. We also demonstrate that our matching technique successfully reproduces the aligned rotator force-free solution. Our new techniques are suitable for studying electromagnetic effects and predicting electromagnetic signals arising in many different curved spacetime scenarios. For example, we can treat spinning neutron stars, either in isolation or in compact binaries, that have MHD interiors and force-free magnetospheres.