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We investigate the dynamics of a circumbinary disc that responds to the lossof mass and to the recoil velocity of the black hole produced by the merger ofa binary system of supermassive black holes. We perform the firsttwo-dimensional general relativistic hydrodynamics simulations of\textit{extended} non-Keplerian discs and employ a new technique to construct a"shock detector", thus determining the precise location of the shocks producedin the accreting disc by the recoiling black hole. In this way we can study howthe properties of the system, such as the spin, mass and recoil velocity of theblack hole, affect the mass accretion rate and are imprinted on theelectromagnetic emission from these sources. We argue that the estimates of thebremsstrahlung luminosity computed without properly taking into account theradiation transfer yield cooling times that are unrealistically short. At thesame time we show, through an approximation based on the relativisticisothermal evolution, that the luminosity produced can reach a peak value above$L \simeq 10^{43} \ {\rm erg/s} $ at about $\sim 30\,{\rm d}$ after the mergerof a binary with total mass $M\simeq 10^6 M_\odot$ and persist for several daysat values which are a factor of a few smaller. If confirmed by moresophisticated calculations such a signal could indeed lead to anelectromagnetic counterpart of the merger of binary black-hole system.

EM counterparts of recoiling black holes: general relativistic simulations of non-Keplerian discs