Breakdown of force-free electrodynamics in electric zones

It is shown that force-free electrodynamics (FFE) breaks down in regions where $B^2 -E^2 <0$ (electric zones) even if $\pmb{E}\cdot\pmb{B} =0$. Spontaneous creation of such will inevitably lead to plasma oscillations subsequently decay over a few periods via anomalous heating and, under certain conditions, emission high energy quanta, until the system relaxes state which $B^2-E^2 \sim 0$. For M87, assuming pair with order unity multiplicity, inverse Compton cooling time estimated be shorter than dynamical when $E^2/B^2-1 > (10^4/\sigma)^2$ roughly, $\sigma$ magnetization. If electric zone weak, global maintain nearly state, however, condition, $F^{\mu\nu}J_\nu=0$, broken at access field and cannot describe wave dynamics. Our analysis does not support recent claims, zones can trigger transition turbulence which, generated ergosphere Kerr black hole, extraction hole rotational energy. Whether some secondary electromagnetic modes produced decaying extract BH yet an open question.