This thesis contains a thorough investigation of the transfer of radiation in spherically symmetric accretion flows onto compact objects within a variety of different assumptions. Although they rely on such a common framework, each of the following three chapters will deal with a different and specific aspect of relativistic radiation hydrodynamics, namely the effects of dynamical comptonization in spherical flows, the study of the thermal structure and the formation of the spectrum in atmospheres of neutron stars accreting at low rates and the stability properties of time-dependent, spherical accretion onto black holes. All but the last of these topics have been carefully investigated having in mind their possible application to certain classes of astrophysical sources in which they could be of importance. In this respect, as it will be discussed in sections 1.2 and 1.3, the results contained in the second and third chapters could be relevant in connection with the observed phenomenology of bright Low Mass X-ray Binaries accreting near the Eddington limit and with the detectability issue of Old isolated Neutron Stars accreting from the interstellar medium. The first part of this introductory chapter (section 1.1) contains a brief review of the derivation of the relativistic radiation hydrodynamics equations in spherical symmetry which will be extensively applied in the remainder of this thesis to the study of the transfer of radiation in accretion flows onto compact objects. In sections 1.2 and 1.3, we will briefly sketch the present observational status and theoretical understanding of bright Low Mass X-ray Binaries (LMXBs) and Old isolated Neutron Stars ( ONSs ). We argue that the spectral effects of dynamical comptonization produced by bulk motion in a radial inflow can be of importance in explaining the high energy tails of the spectra emitted by LMXBs and that radiative transfer calculations in spherical symmetry can be assumed valid in describing the emission properties of ONSs, provided that the effects of the reduced emitting area are taken into account.
