Spinning bodies in General Relativity

TL;DR

This paper develops a covariant Hamiltonian framework for modeling the dynamics of spinning bodies in curved spacetime, enabling analysis of various interactions and derivation of motion equations and conserved quantities.

Contribution

It introduces a flexible Hamiltonian formalism for spinning bodies in General Relativity, including minimal and non-minimal cases, with derivations of equations of motion and constants of motion.

Findings

Framework accommodates various spin interactions

Derivation of equations of motion from energy-momentum tensor

Identification of background-dependent and independent constants of motion

Abstract

A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and interactions of spinning bodies. The dynamics for a minimal and a specific non-minimal hamiltonian is discussed. An independent derivation of the equations of motion from an appropriate energy-momentum tensor is provided. It is shown how to derive constants of motion, both background-independent and background-dependent ones.