  High energy emission from blazars is thought to arise in a relativistic jet
launched by a supermassive black hole. The emission site must be far from the
hole and the jet relativistic, in order to avoid absorption of the photons. In
extreme cases, rapid variability of the emission suggests that structures of
length-scale smaller than the gravitational radius of the central black hole
are imprinted on the jet as it is launched, and modulate the radiation released
after it has been accelerated to high Lorentz factor. We propose a mechanism
which can account for the acceleration of the jet, and for the rapid
variability of the radiation, based on the propagation characteristics of
large-amplitude waves in charge-starved, polar jets. Using a two-fluid
(electron-positron) description, we find the outflows exhibit a delayed
acceleration phase, that starts at roughly 1pc, where the inertia associated
with the wave currents becomes important. The time-structure imprinted on the
jet at launch modulates photons produced by the accelerating jet provided the
pair multiplicity in the black-hole magnetosphere is sufficiently small,
suggesting that very rapid variability is confined to sources in which the
electromagnetic cascade in the black-hole magnetosphere is not prolific.
