I will provide an overview of the equations describing the motion of a small, compact, spinning object in some given background, in general relativity.
I will discuss their derivation, their physical interpretation, their well-posedness, and a formulation as a Hamiltonian system. The main point is to give up-to-date results and references on the matter, so as to encourage listeners to use and explore these simple equations that go beyond the classical geodesic motion around black holes.
Symplectic mechanics of spinning particles in general relativity
Paul Ramond