A gravitational spin-orbit interaction in Poincaré gauge theory

TL;DR

This work develops a cubic-order Poincaré gauge theory (PG) framework to probe gravitational spin-orbit interaction (SOI) and derives axisymmetric field equations under stability-constrained conditions. Focusing on a degenerate model that removes axial kinetic terms, the authors obtain an analytic slow-rotation solution in which the metric remains Kerr-like ($\Psi(r)=1-2m/r$) but the action contains a gravitational SOI term coupling the intrinsic spin $\kappa_{ m s}$ to the extrinsic rotation parameter $a$ through a function $G(r,\vartheta)$ (via $\mathcal{L}_{SOI}$). The interaction is encoded in the axial torsion sector and implies nongeodesic effects for Dirac particles coupled to torsion, while the Kerr geometry is preserved; the paper also argues that nondegenerate PG models could drive novel geometries beyond Kerr, albeit with substantial mathematical challenges. These results establish a concrete mechanism for gravitational SOI in PG theory and motivate further exploration of nondegenerate models to uncover richer beyond-Kerr phenomenology.

Abstract

We show a gravitational spin-orbit interaction that can potentially modify the space-time geometry naturally emerges in the framework of Poincaré gauge theory. For this purpose, we derive the field equations of a particular model with cubic order invariants and demonstrate the existence of analytical solutions which display an interaction between the intrinsic and extrinsic angular momentum parameters in the gravitational action, in analogy to the spin-orbit interaction arising from atomic and nuclear systems. Due to the highly nonlinear character of the field equations under stationary and axisymmetric conditions, we focus on a degenerate case which simplifies their complexity, at the cost of constraining the geometry to the Kerr space-time. Thereby, our results indicate more general solutions with a spin-orbit interaction beyond the Kerr space-time are expected to arise in the nondegenerate models of Poincaré gauge theory.