A New Formulation for General Relativistic Force-Free Electrodynamics and Its Applications

Abstract

We formulate the general relativistic force-free electrodynamics in a new 3 + 1 language. In this formulation, when we have properly defined electric and magnetic fields, the covariant Maxwell equations could be cast in the traditional form with new vacuum constitutive constraint equations. The fundamental equation governing a stationary, axisymmetric force-free black hole magnetosphere is derived using this formulation which recasts the Grad-Shafranov equation in a simpler way. Compared to the classic 3+1 system of Thorne and MacDonald, the new system of 3+1 equations is more suitable for numerical use for it keeps the hyperbolic structure of the electrodynamics and avoids the singularity at the event horizon. This formulation could be readily extended to non-relativistic limit and find applications in flat spacetime. We investigate its application to disk wind, black hole magnetosphere and solar physics in both flat and curved spacetime.