An exact but simple general relativistic model for the gravitational field of active galactic nuclei is constructed, based on the superposition in Weyl coordinates of a black hole, a Chazy-Curzon disk and two rods, which represent matter jets. The influence of the rods on the matter properties of the disk and on its stability is examined. We find that in general they contribute to destabilize the disk. Also the oscillation frequencies for perturbed circular geodesics on the disk are computed, and some geodesic orbits for the superposed metric are numerically calculated.714