Line-driven winds in the presence of strong gravitational fields

We propose a general physical mechanism which could contribute to the formation of fast line-driven outflows at the vicinity of strong gravitational field sources. We argue that the gradient of the gravitational potential plays the same role as the velocity gradient plays in the Sobolev approximation. Both the Doppler effect and gravitational redshifting are taken into account in the Sobolev approximation. The radiation force becomes a function of the local velocity gradient and the gradient of the gravitational potential. The derived equation of motion has a critical point that is different from that of Castor, Abbott and Klein (CAK). A solution, which is continuous through the singular point, is obtained numerically. A comparison with CAK theory is presented. It is shown that the developed theory predicts terminal velocities which are greater than those obtained from the CAK theory.