Time-dependent, force-free, degenerate electrodynamics

Abstract

This paper formulates time-dependent, force-free, degenerate electrodynamics as a hyperbolic system of conservations laws. It is shown that this system has four characteristic modes, a pair of fast waves propagating with the speed of light and a pair of Alfvén waves. All of these modes are linearly degenerate. The results of this analytic study can be used in developing upwind numerical schemes for the electrodynamics of black hole and pulsar magnetospheres. As an example, this paper describes a simple one-dimensional numerical scheme based on linear and exact Riemann solvers.