Trajectories of light beams in a Kerr metric: the influence of the rotation of an observer on the shadow of a black hole

This paper investigates the trajectories of light beams in a Kerr metric, which describes the gravitational field in the neighborhood of a rotating black hole. After reduction by cyclic coordinates, this problem reduces to analysis of a Hamiltonian system with two degrees of freedom. A bifurcation diagram is constructed and a classification is made of the types of trajectories of the system according to the values of first integrals. Relations describing the boundary of the shadow of the black hole are obtained for a stationary observer who rotates with an arbitrary angular velocity about the axis of rotation of the black hole.