Analytical and Numerical Methods and Test Calculations of One-Dimensional Force--Free Magnetodynamics on Arbitrary Magnetic Surfaces across Horizons of Spinning Black Holes

TL;DR

This paper reviews analytical and numerical methods for one-dimensional force-free magnetodynamics around spinning black holes, demonstrating their effectiveness through test simulations on various magnetic surfaces.

Contribution

It introduces a comprehensive review of 1D FFMD techniques and presents test simulation results for different magnetic surface configurations.

Findings

Effective analysis of magnetic field dynamics around black holes.

Validation of 1D FFMD methods through simulation tests.

Insights into electromagnetic processes near spinning black holes.

Abstract

Numerical simulations of the force-free magnetodynamics (FFMD) of the electromagnetic field around a spinning black hole are useful to investigate the dynamic electromagnetic processes around a spinning black hole, such as the emergence of the Blandford--Znajek mechanism. To reveal the basic physics of magnetic fields around a black hole through the dynamic process, we use one-dimensional (1D) FFMD along the axisymmetric magnetic surface, which provides a relatively simple, sufficiently precise, and powerful tool to analyze the dynamic process around a spinning black hole. We review the analytic and numerical aspects of 1D FFMD for an arbitrary magnetic surface around a black hole. In addition, we also show some numerical simulation test results for three types of magnetic surfaces at the equatorial plane of the black hole.