# A gravitational spin-orbit interaction in Poincar\'e gauge theory

## TL;DR

This paper demonstrates a gravitational spin-orbit interaction within Poincaré gauge theory, deriving solutions that suggest modifications to space-time geometry influenced by intrinsic angular momentum.

## Contribution

It introduces a new model with cubic invariants in Poincaré gauge theory that exhibits a gravitational spin-orbit interaction, extending understanding beyond Kerr solutions.

## Key findings

- Analytical solutions showing spin-orbit interaction in Poincaré gauge theory
- Simplification to Kerr space-time in degenerate cases
- Indication of more general solutions with spin-orbit effects

## Abstract

We show a gravitational spin-orbit interaction that can potentially modify the space-time geometry naturally emerges in the framework of Poincar\'e 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 Poincar\'e gauge theory.