On a Representation of Mathisson-Papaetrou-Dixon Equations in the Kerr Metric

TL;DR

This paper presents a new form of the Mathisson-Papapetrou-Dixon equations in the Kerr metric that avoids third-order derivatives, facilitating computer simulations of spinning particles in curved spacetime.

Contribution

A novel representation of the equations that simplifies numerical integration by eliminating third-order derivatives, enabling detailed studies of spin-curvature effects.

Findings

New equation form suitable for computer simulations

Elimination of third-order derivatives in the equations

Enhanced ability to study spin effects in Kerr spacetime

Abstract

New representation of the exact Mathisson-Papapetrou-Dixon equations at the Mathisson-Pirani condition in the Kerr metric which does not contain the third-order derivatives of the coordinates of a spinning particle is obtained. 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 of further investigations of the influence of the spin-curvature interaction on the particle's behavior in the gravitational field without restrictions on its velocity and spin orientation.