Carroll hydrodynamics with spin

TL;DR

This paper develops a framework for Carroll hydrodynamics incorporating spin currents by taking the non-relativistic limit of relativistic hydrodynamics, connecting it to models used in quark-gluon plasma physics.

Contribution

It introduces a method to include spin currents in Carroll hydrodynamics via the c→0 limit of relativistic models with spin, extending the understanding of ultrarelativistic fluid models.

Findings

Derived Carroll hydrodynamics with spin from relativistic models.

Connected boost-invariant models like Bjorken and Gubser flows to Carroll hydrodynamics with spin.

Provided a geometric interpretation of ultrarelativistic fluids in the Carrollian limit.

Abstract

We formulate Carroll hydrodynamics with the inclusion of a spin current. Our strategy relies on the fact that the $c\to 0$ limit of relativistic hydrodynamics yields the equations of Carroll hydrodynamics. Starting with the pre-ultralocal parametrization of the background geometry and the hydrodynamic degrees of freedom for a relativistic fluid endowed with a spin current, the $c\to 0$ limit produces Carroll hydrodynamics with spin. It is known that boost-invariant hydrodynamic models for ultrarelativistic fluids relevant for the physics of quark-gluon plasma, such as Bjorken and Gubser flow, are manifestations of Carroll hydrodynamics under appropriate geometric choices for the underlying Carrollian structure. In this work, we further this mapping between such boost-invariant models and Carroll hydrodynamics, now with the inclusion of a spin current.