  Accretion disks around stellar-mass black holes (BHs) emit radiation peaking
in the soft X-rays when the source is in the thermal state. The emerging
photons are polarized and, for symmetry reasons, the polarization integrated
over the source is expected to be either parallel or perpendicular to the
(projected) disk symmetry axis, because of electron scattering in the disk.
However, due to General Relativity effects photon polarization vectors will
rotate with respect to their original orientation, by an amount depending on
both the BH spin and the observer's inclination. Hence, X-ray polarization
measurements may provide important information about strong gravity effects
around these sources. Along with the spectral and polarization properties of
radiation which reaches directly the observer once emitted from the disk, in
this paper we also include the contribution of returning radiation, i.e.
photons that are bent by the strong BH gravity to return again on the disk,
where they scatter until eventually escaping to infinity. A comparison between
our results and those obtained in previous works by different authors show an
overall good agreement, despite the use of different code architectures. We
finally consider the effects of absorption in the disk material by including
more realistic albedo profiles for the disk surface. Our findings in this
respect show that considering also the ionization state of the disk may deeply
modify the behavior of polarization observables.
