Motion of a spinning particle in curved space-time

TL;DR

This paper develops a covariant Hamiltonian formalism to describe the motion of spinning particles in curved space-time, including minimal and non-minimal Hamiltonians, and discusses implications like the ISCO.

Contribution

It introduces a model-independent Poisson-Dirac bracket approach to derive equations of motion for spinning particles in curved space-time, including gravitational Stern-Gerlach effects.

Findings

Derived equations of motion for spinning particles.

Included gravitational Stern-Gerlach force in the model.

Discussed implications for innermost stable circular orbit (ISCO).

Abstract

The motion of spinning test-masses in curved space-time is described with a covariant hamiltonian formalism. A large class of hamiltonians can be used with the model- independent Poisson-Dirac brackets, to obtain equations of motion. Here we apply it to the minimal hamiltonian and also to a non-minimal hamiltonian, describing the gravi- tational Stern-Gerlach force. And a note on ISCO has been added.