Analytic solution of the Mathisson–Papapetrou–Dixon equations

Derive an analytic solution of the coupled, nonlinear Mathisson–Papapetrou–Dixon equations governing the momentum, spin, and velocity of a spinning extended object in curved spacetime.

Background

The paper models spinning extended objects using the Mathisson–Papapetrou–Dixon equations together with the Tulczyjew–Dixon condition and conserved mass and spin. These equations form a highly coupled nonlinear system for the object’s momentum, spin tensor, and four-velocity. The paper states that no analytic solution is known and therefore relies on perturbative and numerical methods to study finite-size effects and gravitational-memory imprints along the worldline.