  We present a model of optically thin, two-temperature, accretion flows using
an exact Monte Carlo treatment of global Comptonization, with seed photons from
synchrotron and bremsstrahlung emission, as well as with a fully general
relativistic description of both the radiative and hydrodynamic processes. We
consider accretion rates for which the luminosities of the flows are between
~0.001 and 0.01 of the Eddington luminosity. The black hole spin parameter
strongly affects the flow structure within the innermost 10 gravitational
radii. The resulting large difference between the Coulomb heating in models
with a non-rotating and a rapidly rotating black hole is, however, outweighed
by a strong contribution of compression work, much less dependent on spin. The
consequent reduction of effects related to the value of the black spin is more
significant at smaller accretion rates. For a non-rotating black hole, the
compressive heating of electrons dominates over their Coulomb heating, and
results in an approximately constant radiative efficiency of approximately 0.4
per cent in the considered range of luminosities. For a rapidly rotating black
hole, the Coulomb heating dominates, the radiative efficiency is ~1 per cent
and it slightly increases (but less significantly than estimated in some
previous works) with increasing accretion rate. We find an agreement between
our model, in which the synchrotron emission is the main source of seed
photons, and observations of black-hole binaries in their hard states and AGNs
at low luminosities. In particular, our model predicts a hardening of the X-ray
spectrum with increasing luminosity, as indeed observed below ~0.01 of the
Eddington luminosity in both black-hole binaries and AGNs. Also, our model
approximately reproduces the luminosity and the slope of the X-ray emission in
Cen A.
