Rotation of intrinsic orbital angular momentum and the orbital Hall effect for twisted particles in arbitrary gravitational fields

TL;DR

This work derives an exact general equation for the rotation of intrinsic orbital angular momentum (OAM) of twisted particles in arbitrary gravitational fields by casting the dynamics in terms of gravitoelectromagnetic fields $\bm{\mathcal{E}}$ and $\bm{\mathcal{B}}$ within local Lorentz frames. The central result is the lab-frame OAM precession law $\frac{d\hat{\boldsymbol{L}}}{dt}=\bm{\Omega}\times\hat{\boldsymbol{L}}$ with $\bm{\Omega}=-\frac{1}{u^{0}}\big(\bm{\mathcal{B}}-\hat{\boldsymbol{\beta}}\times\bm{\mathcal{E}}\big)$, enabling a general description of the gravitational orbital Hall effect and potential weak-equivalence principle (WEP) violations for OAM. The paper highlights observational regimes in stationary spacetimes (e.g., Lense–Thirring and Kerr) where the orbital Hall effect is measurable and, due to large possible OAM quantum numbers $\ell$, may produce stronger effects than spin-based analogs via a gravitational Stern–Gerlach force $F_{SG}^{(OAM)}=-\nabla(\bm{\Omega}\cdot\hat{\boldsymbol{L}})$. It also analyzes multirefringence of twisted beams and discusses practical implications for astrophysics and precision experiments, noting that Maxwell equations in curved spacetime are unnecessary for twisted photons in this framework.

Abstract

For twisted particles in arbitrary gravitational fields, the problems of the rotation of intrinsic orbital angular momentum and the orbital Hall effect are solved in the general case. We need not use the Maxwell equations in curved spacetimes for a description of twisted photons. The exact general equation rigorously defining the OAM dynamics in any Riemannian spacetimes is derived. The general description of different manifestations of the orbital Hall effect for any twisted particles is also presented. Our short analysis shows that the results obtained can find important practical applications.