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Rebirth of X-ray polarimetric instruments will have a significant impact onour knowledge of compact accreting sources. The properties of inner-accretingregions of active galactic nuclei (AGNs) or X-ray binary systems (XRBs), suchas black-hole spin, their disc inclination and orientation, shape and size oftheir corona, can be polarimetrically studied, parallelly to the well-knownX-ray spectroscopic and timing techniques. In this work, we provide a newspectropolarimetric numerical estimate of X-rays in the lamp-post coronal modelfor a distant observer, including a polarized reflected radiation from theaccretion disc. The local disc reflection was simulated using the codes TITANand STOKES and includes variable disc ionization as well as Monte Carlotreatment of Compton multiple scatterings. We introduce a relativistic codeKYNSTOKES based on our well-tested KY package that accounts for allrelativistic effects on radiation near a black hole, apart from the returningradiation, and adds a possibility of polarized coronal emission. We study thespectrum, polarization degree and polarization angle at spatial infinity forvarious global system parameters and we demonstrate the difference at infinity,if analytical local reflection computations are used. We newly predict that inthe hard X-rays the reflected component can be 25% polarized and the totalemission can be 9% polarized in the most favourable, yet realisticconfigurations of radio-quiet AGNs. Thus, the relativistic disc reflectionremains important for the interpretation of X-ray polarimetric observations.

Spectral and polarization properties of reflected X-ray emission from black-hole accretion discs for a distant observer: the lamp-post model