Mathisson-Papapetrou-Dixon equations in the Schwarzschild and Kerr backgrounds

TL;DR

This paper derives a simplified, third-order derivative-free form of the Mathisson-Papapetrou-Dixon equations for spinning particles in Kerr spacetime, enabling more accurate numerical simulations of spin-curvature effects.

Contribution

It introduces a new representation of the equations that avoids third-order derivatives, facilitating computer integration and analysis of spinning particle dynamics in curved spacetime.

Findings

Derived equations suitable for numerical integration

Analyzed spin-curvature interaction effects

Presented numerical examples in Schwarzschild background

Abstract

A new representation, which does not contain the third-order derivatives of the coordinates, of the exact Mathisson-Papapetrou-Dixon equations, describing the motion of a spinning test particle, is obtained under the assumption of the Mathisson-Pirani condition in a Kerr background. For this purpose the integrals of energy and angular momentum of the spinning particle as well as a differential relationship following from the Mathisson-Papapetrou-Dixon equations are used. The form of these equations is adapted for their computer integration with the aim to investigate the influence of the spin-curvature interaction on the particle's behavior in the gravitational field without restrictions on its velocity and spin orientation. Some numerical examples for a Schwarzschild background are presented.