Linear-order spin corrections to the orbital motion of a spinning particle in Schwarzschild spacetime

Abstract

A test particle moves along a geodesic in curved spacetime. A spinning particle, on the other hand, moves through curved spacetime according the the Mathisson-Papapetrou equations, in which the worldline is accelerated by spin-curvature coupling, and the spin evolution depends on the worldline. In this paper, working in the limit of small spins, we compute the first-order spin correction to the effective potential and orbital frequencies of a spinning particle moving in Schwarzschild spacetime.