  Radio loud active galactic nuclei (AGN) are on average 1000 times brighter in
the radio band compared to radio quiet AGN. We investigate whether this radio
loud/quiet dichotomy can be due to differences in the spin of the central black
holes that power the radio-emitting jets. Using general relativistic
magnetohydrodynamic simulations, we construct steady state axisymmetric
numerical models for a wide range of black hole spins (dimensionless spin
parameter 0.1 <= a <= 0.9999 and a variety of jet geometries. We assume that
the total magnetic flux through the black hole horizon at radius r_H(a) is held
constant. If the black hole is surrounded by a thin accretion disk, we find
that the total black hole power output depends approximately quadratically on
the angular frequency of the hole, P \propto \Omega_H^2 \propto (a/r_H)^2. We
conclude that, in this scenario, differences in the black hole spin can produce
power variations of only a few tens at most. However, if the disk is thick such
that the jet subtends a narrow solid angle around the polar axis, then the
power dependence becomes much steeper, P \propto \Omega_H^4 or even \propto
\Omega_H^6. Power variations of 1000 are then possible for realistic black hole
spin distributions. We derive an analytic solution that accurately reproduces
the steeper scaling of jet power with \Omega_H, and we provide a numerical
fitting formula that reproduces all our simulation results. We discuss other
physical effects that might contribute to the observed radio loud/quiet
dichotomy of AGN.
