We consider the stochastic acceleration of particles which results from
resonant interactions with plasma waves in black hole magnetospheres. We
calculate acceleration rates and escape time scales for protons and electrons
resonating with Alfv\'en waves, and for electrons resonating with whistlers.
Assuming either a Kolmogorov or Kraichnan wave spectrum, accretion at the
Eddington limit, magnetic field strengths near equipartition, and turbulence
energy densities $\sim 10\%$ of the total magnetic field energy density, we
find that Alfv\'en waves accelerate protons to Lorentz factors $\lte
10^4$--$10^6$ before they escape from the system. Acceleration of electrons by
fast mode and whistler waves can produce a nonthermal population of
relativistic electons whose maximum energy is determined by a competition with
radiation losses. Particle energization and outflow is not possible at lower
accretion rates, magnetic field strengths, or turbulence levels due to dominant
Coulomb losses. Increases in the accretion luminosity relative to the Eddington
luminosity can trigger particle acceleration out of the thermal background, and
this mechanism could account for the differences between radio-quiet and
radio-loud active galactic nuclei. Observations of outflowing radio-emitting
components following transient X-ray events in galactic X-ray novae and
gamma-ray flares in blazars are in accord with this scenario.Comment: 31 pages, 8 figures, uuencoded compressed postscript file. Accepted
for publication in The Astrophysical Journal (1 January 1996