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Rapidly rotating bodies moving in curved space-time experience the so-calledspin-curvature force, which becomes important for the motion of compact objectsin gravitational-wave inspirals. In the first approximation, this effect iscaptured in the motion of a spinning test particle. We solve the equationsmotion of a spinning particle to leading order in spin in arbitrary static andspherically symmetric space-times in terms of one-dimensional closed-formintegrals. This solves the problem and proves its integrability in a wide rangeof modified gravities and near exotic compact objects. Then, by specializing tothe case of bound orbits in Schwarzschild space-time, we demonstrate how toexpress the solution in the form of Jacobi elliptic functions.

Analytic solutions for the motion of spinning particles near spherically symmetric black holes and exotic compact objects