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A general physical mechanism of the formation of line-driven winds at the vicinity of strong gravitational field sources is investigated in the frame of General Relativity. We argue that gravitational redshifting should be taken into account to model such outflows. The generalization of the Sobolev approximation in the frame of General Relativity is presented. We consider all processes in the metric of a nonrotating (Schwarzschild) black hole. The radiation force that is due to absorbtion ofdoi:10.1086/427745 fatcat:e22pe6b3vffahfqg5jxsvrx5ti