The motion of a black hole (BH) induces a strong response from the surrounding stellar population. We recall the case of an analytical harmonic potential where half of the stars on circular orbits in that potential shift to an orbit of lower energy, while the other half receive a positive boost and recede to a larger radius. The black hole itself remains on an orbit of fixed amplitude and merely acts as a catalyst for the evolution of the stellar energy distribution function f(E). Numerical integration with a response code show that this effect is operative out to a radius of ~3 to 4 times the radius of influence of the BH RBH. The results for the kinematic signature of BH motion are not sensitive to the shape of the potential and the temperature of the stars measured with Toomre's Q parameter. We report on the evolution of fully self-gravitating systems when damping of the BH orbit is way off the expected exponential decay obtained from the Chandrasekhar formula, a possible result from energy exchanges with the background stars.