  Hot accretion flows such as advection-dominated accretion flows are generally
optically thin in the radial direction. Thus photons generated at some radii
can cool or heat electrons at other radii via Compton scattering. Such global
Compton scattering has previously been shown to be important for the dynamics
of accretion flows. Here, we extend previous treatments of this problem by
using accurate global general relativistic Monte Carlo simulations. We focus on
an inner region of the accretion flow (R < 600R_g), for which we obtain a
global self-consistent solution. As compared to the initial, not
self-consistent solution, the final solution has both the cooling rate and the
electron temperature significantly reduced at radii >=10 gravitational radii.
On the other hand, the radiation spectrum of the self-consistent solution has
the shape similar to that of the initial iteration, except for the high-energy
cut-off being at an energy lower by a factor of ~2 and the bolometric
luminosity decreased by a factor of ~2. We also compare the global Compton
scattering model with local models in spherical and slab geometry. We find that
the slab model approximates the global model significantly better than the
spherical one. Still, neither local model gives a good approximation to the
radial profile of the cooling rate, and the differences can be up to two orders
of magnitude. The local slab model underestimates the cooling rate at outer
regions whereas it overestimates that rate at inner regions. We compare our
modelling results to observed hard-state spectra of black-hole binaries and
find an overall good agreement provided any disc outflow is weak. We find that
general-relativistic effects in flows which dynamics is modified by global
Comptonization is crucial in approaching this agreement.
