  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 of the radiation flux in lines is
derived. It is demonstrated that if gravitational redshifting is taken into
account, the radiation force becomes a function of the local velocity gradient
(as in the standard line-driven wind theory) and the gradient of $g_{00}$. We
derive a general relativistic equation of motion describing such flow. A
solution of the equation of motion is obtained and confronted with that
obtained from the Castor, Abbott & Klein (CAK) theory. It is shown that the
proposed mechanism could have an important contribution to the formation of
line-driven outflows from compact objects.
