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Carroll hydrodynamics with spin

Ashish Shukla, Rajeev Singh, Pushkar Soni

TL;DR

This work constructs Carroll hydrodynamics with a spin current by performing the $c\to 0$ limit of relativistic spin hydrodynamics using a covariant Pre-ultralocal (PUL) framework, yielding an ideal Carroll fluid equipped with a spin current on Carrollian manifolds. It provides the Carroll energy-momentum tensor and a covariant evolution equation for the Carroll spin density, highlighting how background torsion sources spin non-conservation in the Carroll limit and establishing the conformal constraint $\varepsilon=3p$ with $\nabla_\mu\Phi^\mu=0$ in the spin sector. The paper further demonstrates how Bjorken and Gubser boost-invariant flows with spin arise as Carrollian realizations by choosing suitable Carroll geometric data and spin configurations, and it gives explicit mappings for the spin degrees of freedom in these flows. These results open avenues for extending Carroll spin hydrodynamics to include derivative corrections, generating functional formulations, and potential applications to spin polarization phenomena in quark-gluon plasma and related condensed-matter systems.

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.

Carroll hydrodynamics with spin

TL;DR

This work constructs Carroll hydrodynamics with a spin current by performing the limit of relativistic spin hydrodynamics using a covariant Pre-ultralocal (PUL) framework, yielding an ideal Carroll fluid equipped with a spin current on Carrollian manifolds. It provides the Carroll energy-momentum tensor and a covariant evolution equation for the Carroll spin density, highlighting how background torsion sources spin non-conservation in the Carroll limit and establishing the conformal constraint with in the spin sector. The paper further demonstrates how Bjorken and Gubser boost-invariant flows with spin arise as Carrollian realizations by choosing suitable Carroll geometric data and spin configurations, and it gives explicit mappings for the spin degrees of freedom in these flows. These results open avenues for extending Carroll spin hydrodynamics to include derivative corrections, generating functional formulations, and potential applications to spin polarization phenomena in quark-gluon plasma and related condensed-matter systems.

Abstract

We formulate Carroll hydrodynamics with the inclusion of a spin current. Our strategy relies on the fact that the 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 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.
Paper Structure (14 sections, 117 equations, 1 figure)

This paper contains 14 sections, 117 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Carroll hydrodynamics and spin currents
  3. Relativistic hydrodynamics with a spin current
  4. Pre-ultralocal (PUL) parametrization and the $c\to 0$ limit
  5. Carroll hydrodynamics with a spin current
  6. Mapping to Bjorken and Gubser flow with spin
  7. Bjorken flow with a spin current
  8. Gubser flow with a spin current
  9. From Carroll hydrodynamics to Bjorken and Gubser flow with spin
  10. Discussion and outlook
  11. PUL decomposition of the relativistic hydrodynamic equations
  12. Local Carroll boost invariance of the hydrodynamic equations
  13. Spin current in the Papapetrou-Randers parametrization
  14. Maps to Bjorken and Gubser flow

Figures (1)

  • Figure 1: Depiction of the heavy-ion collision process. The collision happens at time $t=0$ at the origin. Without loss of generality, one can align the $z$-axis long the beam direction, while the $(x,y)$-axes form the transverse plane. The Milne patch of the Minkowski spacetime, covered by the proper time, rapidity coordinates $(\tau, \rho)$, serves as the forward lightcone for the collision event.