Gravitating discs around a Schwarzschild black hole: I

We study the class of Lemos-Letelier annular discs (realistic gravitating s tatic axisymmetric thin discs obtained by inversion of the first Morgan-Mor gan 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 interpret ed by counter-rotating streams of particles on stable timelike geodesics. O ne can then consider a sequence of stable physical discs with different mas ses and inner rims at the corresponding least possible radii. The basic pro perties of this sequence are shown on positions of the inner rims and of im portant circular orbits, on positions of the horizon acid on density and Ke plerian-velocity profiles within the discs, plotted in terms of the Schwarz schild radial coordinate, circumferential radius and proper distance from t he horizon.