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Gravitational interaction of celestial bodies and black holes with particle dark matter

The particles of a dark matter due to gravitational interaction deviate from straight trajectories in the vicinity of a massive body. This causes their density to become inhomogeneous. The developed density contrast causes a gravitation attraction force acting upon the body proportional to its mass squared. Since this effect depends on the body's velocity, it causes a specific reference frame to stand out. The force is similar to an anisotropic drag, which can be negative in some directions. The mean drag force, averaged over all direction, is nonpositive. We can expect some observational manifestation of the considered effect for supermassive black holes in galaxies.