  Using a Monte Carlo method, we derive spectra arising from Comptonization
taking place close to a Kerr black hole. We consider a model consisting of a
hot thermal corona Comptonizing seed photons emitted by a cold accretion disc.
We find that general relativistic effects are crucial for the emerging spectra
in models which involve significant contribution of radiation produced in the
black hole ergosphere. Due to this contribution, spectra of hard X-ray emission
produced in the vicinity of a rapidly rotating black hole strongly depend on
the inclination of the line of sight, with larger inclinations corresponding to
harder spectra. Remarkably, such anisotropy could be responsible for properties
of the X-ray spectra of Seyfert galaxies, which appear to be intrinsically
harder in type 2 objects than in type 1, as reported recently.
