A 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 "multi-block" technique to represent a domain with $S^2\times {\mathbb{R}}^{+}$ topology within a stable finite-differences scheme. ii) We employ as evolution equations those arising from a covariant hyperbolization of the FFE system. 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. We find stationary jet solutions which reach equilibrium --through boundary conditions-- with the outer numerical surface. This is so, even when the outer boundary is located very close to the central region (i.e. $r_{out}\sim 10M$). These numerical solutions reproduce most of the known results for analogue astrophysical settings.

arXiv comment18 pages, 17 figures

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• Magnetosphere of a spinning black hole and the role of the current sheet
• Astrophysical jets from boosted compact objects
• Skylight: a new code for general-relativistic ray-tracing and radiative transfer in arbitrary spacetimes
• Relativistic force-free models of the thermal X-ray emission in millisecond pulsars observed by NICER
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• General relativistic force-free electrodynamics with a discontinuous Galerkin-finite difference hybrid method
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• Safety first: Stability and dissipation of line-tied force-free flux tubes in magnetized coronae
• Generalized split monopole magnetospheres: the effects of current sheets
• Ill-posedness of the mean-field dynamo equations with a linear electromotive force
• Gamma-radiation sky maps from compact binaries
• Particle acceleration driven by null electromagnetic fields near a Kerr black hole