I. A star orbiting around a supermassive rotating black hole: Free motion and corrections due to star-disc collisions

Our aim is to study the evolution of the orbit of a star under the influence of interactions with an accretion disc in an AGN. The model considered consists of a low-mass compact object orbiting a supermassive black hole and colliding periodically with the accretion disc. Approximate calculations based mostly on Newtonian theory of gravity have been carried out by several authors to estimate the effects of circularization of initially eccentric orbits and their dragging to the disc plane. Here, we present the first step to a more adequate general relativistic approach in which the gravitational field of the nucleus is described by the Kerr metric. The star is assumed to move along a geodesic arc between successive interactions with an equatorial accretion disc. We solved relevant formulae for the geodesic motion in terms of elliptic integrals and constructed a fast numerical code which, after specifying details of the star-disc interaction, enables us to follow the trajectory of the star for many revolutions and study the evolution of its eccentricity and inclination with respect to the disc. Lense-Thirring precession of the orbit is potentially a very important effect for observational confirmation of the presence of a rotating black hole in the nucleus. Our approach takes effects of the Lense Thirring precession into account with no approximation. The model of star-disc interactions has been suggested to explain the Xray variability observed in the Seyfert galaxy NGC 6814. We briefly discuss on this subject.