Spinning massive test particles in cosmological and general static spherically symmetric spacetimes

Understand

A Lagrangian formalism is used to study the motion of a spinning massive particle in Friedmann--Robertson--Walker and G\"odel spacetimes, as well as in a general Schwarzschild-like 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 time independent, and a different constant otherwise.