The interaction between graviton spin and gravitomagnetic fields

TL;DR

This paper provides a detailed mathematical analysis of how graviton spin interacts with gravitomagnetic fields, deriving an explicit expression for the coupling in the context of weak gravitational fields.

Contribution

It introduces a specific mathematical expression for graviton spin-gravitomagnetic coupling within the Lagrangian/Hamiltonian framework for weak gravitational fields.

Findings

Derived an explicit coupling expression involving metric components and their derivatives.

Clarified the mathematical structure of graviton spin interactions with gravitomagnetic fields.

Contributed to the theoretical understanding of graviton interactions in weak gravity regimes.

Abstract

This note is devoted to the detailed mathematical treatment of the coupling of graviton spin to gravitomagnetic fields. The expression (i.e., $\sim g_{0m}\dot{g}_{0n}(\partial_{m}g_{0n}-\partial_{n}g_{0m})$) for the graviton spin-gravitomagnetic (S-G) coupling in the Lagrangian/Hamiltonian density of the weak gravitational fields is presented in this note.