Spin hydrodynamics on a hyperbolic expanding background

TL;DR

This paper investigates relativistic spin hydrodynamics on a hyperbolic expanding background, deriving exact evolution equations and revealing unique oscillatory behavior of spin components, thus establishing a new benchmark for finite-support relativistic fluid models.

Contribution

It derives exact spin evolution equations on a hyperbolic background and highlights distinctive oscillatory spin behavior, contrasting with previous models like Gubser flow.

Findings

Enhanced localization of spin dynamics due to rapid early expansion.

Oscillation of azimuthal spin component in the forward lightcone.

Establishment of the $$ background as a new benchmark for spin hydrodynamics.

Abstract

We study relativistic spin hydrodynamics on the hyperbolic $\kappa=-1$ flow background recently identified by Grozdanov. This background corresponds to an $SO(2,1)$-invariant, transversely expanding solution with finite spacetime support in Minkowski space, in contrast to the well-known Gubser flow $(\kappa=+1)$ which possesses $SO(3)$ symmetry and infinite transverse extent. Working within the formulation of perfect-fluid spin hydrodynamics, we derive the exact evolution equations for all spin components of the spin potential on the $\kappa=-1$ background. We find that the enhanced early-time expansion rate and the presence of a causal edge lead to a stronger localization of spin dynamics compared to the Gubser case. Remarkably, the azimuthal component of the spin potential oscillates as it decays in the forward lightcone, in stark contrast to the Gubser flow. Thus, our results establish the $\kappa=-1$ flow as a distinct and physically meaningful benchmark for studying spin dynamics in expanding relativistic fluids with finite spacetime support.