Numerical solution of Mathisson-Papapetrou-Dixon equations for spinning test particles in a Kerr metric

Abstract

In this work we calculate some estimations of the gravitomagnetic clock effect, taking into consideration not only the rotating gravitational field of the central mass, but also the spin of the test particle, obtaining values for $\Delta t=t_{+}-t_{-}=2.5212079035\times10^{-8} \textrm{s}$. We use the formulation of Mathisson-Papapetrou-Dixon equations for this problem in a Kerr metric. In order to compare our numerical results with previous works, we consider initially only the equatorial plane and also apply the Mathisson-Pirani supplementary spin condition for the spinning test particle.