Fast Wave Polarization, Charge Horizons and the Time Evolution of Force-Free Magnetospheres

Numerical simulations of force-free, degenerate (ffde)pulsar and black hole magnetospheres are often based on 1-D characteristics. In particular, the plasma wave polarizations that can be propagated along the 1-D characteristics determine the time evolution of the entire system. There are two sets of characteristics,corresponding to the fast and Alfven modes. The fast wave is generally considered to be a transverse light wave, however recently it has been claimed that light-like fast waves can transport a longitudinal electric polarization, $E_{\parallel}$, at the speed of light. The implication is quite profound if true, namely that the wrong information has been propagated along the fast characteristics in all previous simulations of force-free magnetospheres. It is shown in this Letter that the light-like fast waves must be transverse and previous simulations are valid. This result is demonstrated by means of a fundamental physical principle (associated with the fact that particles cannot flow faster than the speed of light), there exists a charge horizon in ffde magnetospheres. It is shown that the Alfven critical surfaces in a ffde magnetosphere are both charge and particle horizons, i.e. one way membranes that do not permit traversal by charges nor particles anti-directed to the bulk flow. Since the propagation of a discontinuous change in $E_{\parallel}$ requires a physical surface charge on the wave-face, it is also a one-way membrane for longitudinally polarized waves. Besides justifying previous ffde simulations this result also invalidates previous claims that fast waves can radiate $E_{\parallel}$ from the event horizon of a black hole.