Force Free Waves and Black Hole Magnetospheric Causality

Abstract

The force free approximation is often useful when describing tenuous plasmas in strong cosmic magnetic fields. Time evolution of any such system is governed by the information that can be transported along the characteristics of the plasma modes allowed by the force free constraint. This brief article elucidates, for the first time, the nature of the information that can be transported along the characteristics for each of the two plasma modes, the Alfven and fast modes. It is reassuring that these modes behave as one would expect if the perfect magnetohydrodynamic (MHD) modes in a magnetically dominated plasma were evaluated in the limit of zero plasma inertia (i.e., only allowed to propagate information consistent with the force free constraint). There are no properties of these waves that do not exist within the MHD theory, when this additional constraint on the current is imposed. The results of the characteristic analysis elucidates the nature of the causality violation in force free black hole magnetospheres. The most significant result from the standpoint of global causality is that charge and current perturbations can not be transported along the fast mode short wavelength characteristics in the force free limit.