Algebraic computing and the geodesics of the Kerr metric

Abstract

Using algebraic computing, a given algorithm is solved to reproduce easily the well-known results concerning the equatorial test particle’s motion in the background of the Kerr metric. As another application, the radii of the equatorial circular null geodesics in the Kerr–Newman and Kerr metrics are calculated. Furthermore, this approach can be easily extended to study the equatorial timelike and null geodesics in any axisymmetric and stationary metric.