Gravitating discs around a Schwarzschild black hole:: I

We study the class of Lemos-Letelier annular discs (realistic gravitating static axisymmetric thin discs obtained by inversion of the first Morgan-Morgan solution) around Schwarzschild black holes. For each value of the inner radius, the range of masses is found when all of the disc can be interpreted by counter-rotating streams of particles on stable timelike geodesics. One can then consider a sequence of stable physical discs with different masses and inner rims at the corresponding least possible radii. The basic properties of this sequence are shown on positions of the inner rims and of important circular orbits, on positions of the horizon acid on density and Keplerian-velocity profiles within the discs, plotted in terms of the Schwarzschild radial coordinate, circumferential radius and proper distance from the horizon.