We have described a method to test the overall accuracy of the pseudo-Kerr models of the relativistic gravitational field and we applied our approach to two particular potentials, given by Eqs. (10) and (19). One can conclude that the corresponding equations of motion, (11)-(13) and (20)-(22) respectively, do not provide an acceptable approximation to exact Kerr geodesic equations in the part of the -plane where , and vice-versa. This statement does not apply strictly to all trajectories (with different initial conditions) because our graphs are given in terms of mean values. We suggest that a check of this type should always be employed when some particular form of approximative equations is formulated. For example, calculation of the spectra of accretion discs requires integration of a large number of photon trajectories; the overall accuracy in the description of the gravitational field is then important.
© European Southern Observatory (ESO) 1999
Online publication: March 1, 1999