Hojman, S. A., & Asenjo, F. A. (2017). Spinning particles coupled to gravity and the validity of the universality of free fall. Class. Quantum Gravity, 34(11), 8 pp.
Abstract: Recent experimental work has determined that free falling Rb87 atoms on Earth, with vertically aligned spins, follow geodesics, thus apparently ruling out spingravitation interactions. It is showed that while some spinning matter models coupled to gravitation referenced to in that work seem to be ruled out by the experiment, those same experimental results confirm theoretical results derived from a Lagrangian description of spinning particles coupled to gravity constructed over forty years ago. A proposal to carry out (similar but) different experiments which will help to test the validity of the universality of free fall as opposed to the correctness of the aforementioned Lagrangian theory, is presented.

Zalaquett, N., Hojman, S. A., & Asenjo, F. A. (2014). Spinning massive test particles in cosmological and general static spherically symmetric spacetimes. Class. Quantum Gravity, 31(8), 21 pp.
Abstract: A Lagrangian formalism is used to study the motion of a spinning massive particle in FriedmannRobertsonWalker and Godel spacetimes, as well as in a general Schwarzschildlike spacetime and in static spherically symmetric conformally flat spacetimes. Exact solutions for the motion of the particle and general exact expressions for the momenta and velocities are displayed for different cases. In particular, the solution for the motion in spherically symmetric metrics is presented in the equatorial plane. The exact solutions are found using constants of motion of the particle, namely its mass, its spin, its angular momentum, and a fourth constant, which is its energy when the metric is timeindependent, and a different constant otherwise. These constants are associated to Killing vectors. In the case of the motion on the FriedmannRobertsonWalker metric, a new constant of motion is found. This is the fourth constant which generalizes previously known results obtained for spinless particles. In the case of general Schwarzschildlike spacetimes, our results allow for the exploration of the case of the ReissnerNordstrom(Anti) de Sitter metric. Finally, for the case of the conformally flat spacetimes, the solution is explicitly evaluated for different metric tensors associated to a universe filled with static perfect fluids and electromagnetic radiation. For some combination of the values of the constants of motion the particle trajectories may exhibit spacelike velocity vectors in portions of the trajectories.
