On the possibility of a warped disc origin of the inclined stellar discs at the Galactic Centre

(Abridged) The Galactic Center (GC) hosts a population of young stars some of which seem to form mutually inclined discs of clockwise and counter clockwise rotating stars. We present a warped disc origin scenario for these stars assuming that an initially flat accretion disc becomes warped due to the Pringle instability, or due to Bardeen-Petterson effect, before it fragments to stars. We show that this is plausible if the star formation efficiency $epsilon_{SF} lesssim 1$, and the viscosity parameter $alpha sim 0.1$. After fragmentation, we model the disc as a collection of concentric, circular, mutually tilted rings, and construct warped disc models for mass ratios and other parameters relevant to the GC environment, but also for more massive discs. We take into account the discs self-gravity and the torques exerted by a surrounding star cluster. We show that a self-gravitating low-mass disc ($M_d / M_{bh} sim 0.001$) precesses in integrity in the life-time of the stars, but precesses freely when the torques from a non-spherical cluster are included. An intermediate-mass disc ($M_d / M_{bh} sim 0.01$) breaks into pieces which precess independently in the self-gravity-only case, and become disrupted in the presence of the star cluster torques. For a high-mass disc ($M_d / M_{bh} sim 0.1$) the evolution is dominated by self-gravity and the disc is broken but not dissolved. The time-scale after which the disc breaks scales almost linearly with ($M_d / M_{bh}$) for self-gravitating models. Typical values are longer than the age of the stars for a low mass disc, and are in the range $sim 8 times 10^4-10^5$ yr for high and intermediate-mass discs respectively. None of these models explain the rotation properties of the two GC discs, but a comparison of them with the clockwise disc shows that the lowest mass model in a spherical star cluster matches the data best.