Late-time attractors in relativistic spin hydrodynamics in Gubser flow

TL;DR

This paper analyzes the late-time behavior and attractor structure of spin density in relativistic spin hydrodynamics under Gubser flow, revealing conditions for slow decay and hydrodynamic mode behavior.

Contribution

It derives the differential equation for spin density, identifies attractors and repellers, and maps solutions to flat space to understand decay regimes and hydrodynamic behavior.

Findings

Identified late-time asymptotic solutions and attractors for spin density.

Found parameter regions with power-law decay of spin density.

Demonstrated slow decay of spin components as hydrodynamic modes.

Abstract

We investigate the late-time asymptotic solutions and attractor structure of the spin density in minimal causal spin hydrodynamics in Gubser flow. After deriving the differential equation governing the spin density, we obtain its late-time asymptotic solutions and identify both attractors and repellers in the corresponding numerical solutions. We then map these solutions back to flat Minkowski space and find parameter regions where the spin density exhibits a power-law decay. We further show that, when the characteristic length scale of the system is much larger than the proper time, several components of the spin density can decay as slowly as conventional thermodynamic variables in relativistic hydrodynamics. In this regime, the spin density behaves as a hydrodynamic mode governed by the late-time scaling laws of the flow.