Force‐free Waves and Black Hole Magnetospheric Causality

The force free approximation is often useful when describing tenuous plasmasin strong cosmic magnetic fields. Time evolution of any such system is governedby the information that can be transported along the characteristics of theplasma modes allowed by the force free constraint. This brief articleelucidates, for the first time, the nature of the information that can betransported along the characteristics for each of the two plasma modes, theAlfven and fast modes. It is reassuring that these modes behave as one wouldexpect if the perfect magnetohydrodynamic (MHD) modes in a magneticallydominated plasma were evaluated in the limit of zero plasma inertia (i.e., onlyallowed 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 thecharacteristic analysis elucidates the nature of the causality violation inforce free black hole magnetospheres. The most significant result from thestandpoint of global causality is that charge and current perturbations can notbe transported along the fast mode short wavelength characteristics in theforce free limit.Comment: Accepted by ApJ. This rectifies gross errors in a simple short wavelength force free calculation posted on astro-ph that was intended to discredit the MHD analysis of black hole GH