  We analyze the exact general relativistic exact integro-differential equation
of radiative transfer describing the interaction of low energy photons with a
Maxwellian distribution of hot electrons in gravitational field of a
Schwarzschild black hole. We prove that due to Comptonization an initial
arbitrary spectrum of low energy photons unavoidably results in spectra
characterized by an extended power-law feature. We examine the spectral index
by using both analytical and numerical methods for a variety of physical
parameters as such the plasma temperature and the mass accretion rate. The
presence of the event horizon as well as the behaviour of the null geodesics in
its vicinity largely determine the dependence of the spectral index on the flow
parameters. We come to the conclusion that the bulk motion of a converging flow
is more efficient in upscattering photons than thermal Comptonization provided
that the electron temperature in the flow is of order of a few keV or less. In
this case, the spectrum observed at infinity consists of a soft component
produced by those input photons that escape after a few scatterings without any
significant energy change and of hard component (described by a power law)
produced by the photons that underwent significant upscattering. The luminosity
of the power-law component is relatively small compared to that of the soft
component. For accretion into black hole the spectral energy index of the
power-law is always higher than one for plasma temperature of order of a few
keV. This result suggests that the bulk motion Comptonization might be
responsible for the power-law spectra seen in the black-hole X-ray sources.
