  A "temporal analogue" of the standard Poynting-Robertson effect is analyzed
as induced by a dust of particles (instead of a gas of photons) surrounding a
Schwarzschild black hole. Test particles inside this cloud undergo acceleration
effects due to the presence of a friction force, so that the fate of their
evolution can be completely different from the corresponding geodesic motion.
Typical situations are discussed of hyperbolic motion of particles scattered by
the black hole in the presence of a dust filling the whole spacetime region
outside the horizon as well as particles which free fall radially crossing a
corona located at a certain distance from the horizon. The existence of
equilibrium orbits may prevent particles from either falling into the hole or
escaping to infinity.
