Equatorial geodesic motion in the gravitational field of a rotating source

The purpose of this note is to investigate the geodesic motion in the gravitational field of a rotating source, making use of the exact empty-space solutions of Einstein’s equations given by Kerr. The earlier weak-field approximate solutions of Lense and Thirring for a rotating body are also examined to compare them with the exact case and with the Schwarzschild nonrotating one, whose geodesic properties are also briefly summarized. The behaviour of single orbits, for example the precession of the pericenter, will not be mentioned since they have been extensively analysed in the cited references. The differential equations of the geodesics are analysed from an analytical point of view in order to recognize the shape of the loci of the turning points for the test particles without introducing numerical values of the parameters involved such asa (specific angular momentum of the rotating body) andΓ (test particle’s effective energy). Diagrams are given which show the behaviour of the geodesics for different ranges of these parameters. An attempt to make a physical comparison between these three cases has been done in the last Section.