Pseudo-Newtonian models of a rotating black hole field

A pseudo-Newtonian description of the gravitational field which yields the equations of motion resembling, as closely as possible, the geodesic equati on of general relativity is found for the Kerr spacetime. The potential obt ained consists of three parts, interpreted as a purely Newtonian (gravitoel ectric) term, a dragging (gravitomagnetic) term, and a space-geometry corre ction. The accuracy of the pseudo-Newtonian model is studied by a method wh ich compares, systematically, two large sets of trajectories: geodesics in the Kerr spacetime versus test-particle trajectories in the pseudo-Newtonia n field. It is suggested that every pseudo-Newtonian model should be submit ted to analogous systematic analysis before it is used in astrophysical app lications. A modified Newtonian potential which accounts for the frame-drag ging effects can be a practical tool in studying stationary accretion discs . Non-stationary configurations are more complicated and we will not sugges t to use this approach to such topics in accretion theory as gravitomagneti c oscillations of discs and their relation to quasi-periodic sources.