  Electron-positron pairs may be produced near accreting black holes by a
variety of physical processes, and the resulting pair plasma may be accelerated
and collimated into a relativistic jet. Here we use a self-consistent dynamical
and radiative model to investigate pair production by \gamma\gamma collisions
in weakly radiative accretion flows around a black hole of mass M and accretion
rate \dot{M}. Our flow model is drawn from general relativistic
magnetohydrodynamic simulations, and our radiation field is computed by a Monte
Carlo transport scheme assuming the electron distribution function is thermal.
We argue that the pair production rate scales as r^{-6} M^{-1} \dot{M}^{6}. We
confirm this numerically and calibrate the scaling relation. This relation is
self-consistent in a wedge in M, \dot{M} parameter space. If \dot{M} is too low
the implied pair density over the poles of the black hole is below the
Goldreich-Julian density and \gamma\gamma pair production is relatively
unimportant; if \dot{M} is too high the models are radiatively efficient. We
also argue that for a power-law spectrum the pair production rate should scale
with the observables L_X \equiv X-ray luminosity and M as L_X^2 M^{-4}. We
confirm this numerically and argue that this relation likely holds even for
radiatively efficient flows. The pair production rates are sensitive to black
hole spin and to the ion-electron temperature ratio which are fixed in this
exploratory calculation. We finish with a brief discussion of the implications
for Sgr A* and M87.
