Late-time attractors in relativistic spin hydrodynamics in Gubser flow

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.