Accretion on a fast-moving gravitating centre

The self-similar solution is obtained for the accretion of a gas on a fast-moving centre, modelling a black hole. A shock wave front is presented by a conical surface. The solution is obtained for different adiabatic indices γ and different density distributions of the falling gas far from the centre. It is shown that self-similar solution in which the matter fills up all the space exists only for 1.31 < γ <5/3 for uniform density at infinity and for isolated values of γ for other power distributions of density. In the other cases, there are solutions only with the hollow cone behind the moving centre