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

TL;DR

This paper numerically solves the Mathisson-Papapetrou-Dixon equations for spinning test particles in a Kerr metric to estimate the gravitomagnetic clock effect, incorporating particle spin and comparing with previous results.

Contribution

It presents a numerical approach to solve the equations for spinning particles in Kerr spacetime, including spin effects on the gravitomagnetic clock effect.

Findings

Estimated the gravitomagnetic clock effect with particle spin included

Numerical solutions align with previous theoretical predictions

Analyzed spin contributions in equatorial plane orbits

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.