  Ultra Fast Outflows (UFOs) are an established feature in X-ray spectra of
AGNs. According to the standard picture, they are launched at accretion disc
scales with relativistic velocities, up to 0.3-0.4 c. Their high kinetic power
is enough to induce an efficient feedback on galactic-scale, possibly
contributing to the co-evolution between the central supermassive black hole
(SMBH) and the host galaxy. It is therefore of paramount importance to fully
understand the UFO physics, in particular the forces driving their acceleration
and the relation with the accretion flow they originate from. In this paper we
investigate the impact of special relativity effects on the radiative pressure
exerted onto the outflow. The radiation received by the wind decreases for
increasing outflow velocity v, implying that the standard Eddington limit
argument has to be corrected according to v. Due to the limited ability of the
radiation to counteract the SMBH gravity, we expect to find lower typical
velocities with respect to the non-relativistic scenario. We integrate the
relativistic-corrected outflow equation of motion for a realistic set of
starting conditions. We concentrate on UFO typical values of ionisation, column
density and launching radius. We explore a one-dimensional, spherical geometry
and a 3D setting with a rotating thin accretion disc. We find that the
inclusion of relativistic effects leads to sizeable differences in the wind
dynamics and that v is reduced up to 50% with respect to the non-relativistic
treatment. We compare our results with a sample of UFO from the literature, and
we find that the relativistic-corrected velocities are systematically lower
than the reported ones, indicating the need for an additional mechanism, such
as magnetic driving, to explain the highest velocity components. These
conclusions, derived for AGN winds, have a general applicability.
