  We study the spectra generated as a result of bulk Comptonization by
relativistic electrons in radial flows onto compact objects. We solve
numerically the general-relativistic radiative transfer equation in the
Schwarzschild spacetime, in steady-state and under minimal assumptions. We show
that power-law spectra result from multiple scatterings, in a way similar to
thermal Comptonization. We also find that photon-electron interactions taking
place near the black-hole event horizon affect very little the emerging
spectra. We, therefore, argue that bulk Comptonization spectra do not carry
distinguishing signatures of the compact object around which they are produced.
We examine the dependence of the spectra on simplifications often employed
regarding the spacetime geometry, the distribution of photon sources, and the
boundary conditions. We show that the existence of trapped characteristics
around a black hole reduces the efficiency of Comptonization and that general
relativistic effects identically cancel bulk Comptonization effects for a
free-falling flow and in the limit of infinitesimal mean-free path. As a
result, we find that neglecting the curved spacetime geometry leads to
overestimating the high-energy flux by up to an order of magnitude. Finally, we
demonstrate that the spectrum from accretion onto a neutron star depends
sensitively on the imposed boundary conditions, while that from a black hole is
immune to such choices.
