  The properties of a stationary gas cloud surrounding a black hole are
discussed, assuming that the gas consists of collisionless, identical massive
particles that follow spatially bound geodesic orbits in the Schwarzschild
spacetime. Several models for the one-particle distribution function are
considered, and the essential formulae that describe the relevant macroscopic
observables, like the current density four-vector and the
stress-energy-momentum tensor are derived. This is achieved by rewriting these
observables as integrals over the constants of motion and by a careful analysis
of the range of integration. In particular, we provide configurations with
finite total mass and angular momentum. Differences between these
configurations and their nonrelativistic counterparts in a Newtonian potential
are analyzed. Finally, our configurations are compared to their hydrodynamic
analogues, the "polish doughnuts".
