Context. Radio-loud AGNs with powerful relativistic jets are thought to be associated with rapidly spinning black holes (BHs). BH spin-up may result from a number of processes, including accretion of matter onto the BH itself, and catastrophic events such as BH-BH mergers. Aims. We study the intriguing properties of the powerful (L_bol ~ 10^47 erg s^-1) radio-loud quasar 3C 186. This object shows peculiar features both in the images and in the spectra. Methods. We utilize near-IR Hubble Space Telescope (HST) images to study the properties of the host galaxy, and HST UV and Sloan Digital Sky Survey optical spectra to study the kinematics of the source. Chandra X-ray data are also used to better constrain the physical interpretation. Results. HST imaging shows that the active nucleus is offset by 1.3 +- 0.1 arcsec (i.e. ~11 kpc) with respect to the center of the host galaxy. Spectroscopic data show that the broad emission lines are offset by -2140 +-390 km/s with respect to the narrow lines. Velocity shifts are often seen in QSO spectra, in particular in high-ionization broad emission lines. The host galaxy of the quasar displays a distorted morphology with possible tidal features that are typical of the late stages of a galaxy merger. Conclusions. A number of scenarios can be envisaged to account for the observed features. While the presence of a peculiar outflow cannot be completely ruled out, all of the observed features are consistent with those expected if the QSO is associated with a gravitational wave (GW) recoiling BH. Future detailed studies of this object will allow us to confirm this type of scenario and will enable a better understanding of both the physics of BH-BH mergers and the phenomena associated with the emission of GW from astrophysical sources.
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