Novel scheme for simulating the force-free equations: Boundary conditions and the evolution of solutions towards stationarity

Abstract

Force-free electrodynamics (FFE) describes a particular regime of magnetically dominated relativistic plasmas, which arises on several astrophysical scenarios of interest such as pulsars or active galactic nuclei. In this article, we present a full 3D numerical implementation of the FFE evolution around a Kerr black hole. The novelty of our approach is three-folded: (i) We use the "multiblock" technique [1L. Lehner, O. Reula, and M.Tiglio, Multi-block simulations in general relativity: High-order discretizations, numerical stability and applications, Classical Quantum Gravity 22, 5283 (2005).CQGRDG0264-938110.1088/0264-9381/22/24/006] to represent a domain with S2×R+ topology within a stable finite-differences scheme. (ii) We employ as evolution equations those arising from a covariant hyperbolization of the FFE system [2F. Carrasco and O. Reula, Covariant hyperbolization of force-free electrodynamics, Phys. Rev. D 93, 085013 (2016).PRVDAQ2470-001010.1103/PhysRevD.93.085013]. (iii) We implement stable and constraint-preserving boundary conditions to represent an outer region given by a uniform magnetic field aligned or misaligned respect to the symmetry axis. The construction of appropriate and consistent boundary conditions, both preserving the constraints and physically immersing the system in a uniform magnetic field, has allowed us to obtain long-term stationary solutions representing jets of astrophysical relevance. These numerical solutions are shown to be consistent with previous studies.