Toroidal source around a static black hole

A sequence of exact solutions of Einstein equations is obtained describing the fields of a Schwarzschild black hole surrounded by static, axially symmetric, thick toroids. Its properties are illustrated by plotting the shape of the gravitational field, the deformation of the black-hole horizon and several types of time-like geodesics, in dependence on parameters of the toroid.Dedicated to Professor Jií Horáek on the occasion of his 60th birthday.