Analytic solutions of relativistic dissipative spin hydrodynamics with radial expansion in Gubser flow

TL;DR

This paper derives exact solutions for relativistic dissipative spin hydrodynamics with radial expansion under Gubser flow, providing insights into spin dynamics and decay behaviors in high-energy systems.

Contribution

It presents the first analytic solutions of dissipative relativistic spin hydrodynamics with Gubser expansion, including spin density and potential in both de Sitter and Minkowski spaces.

Findings

Spin density decays as ~L^{-2}τ^{-1} in large L limit.

Spin potential decays as ~L^{-2}τ^{-1/3}.

Non-vanishing spin corrections affect energy density and dissipative terms.

Abstract

We have derived the analytic solutions of dissipative relativistic spin hydrodynamics with Gubser expansion. Following the standard strategy of deriving the solutions in a Gubser flow, we take the Weyl rescaling and obtain the energy-momentum and angular momentum conversation equations in the $dS_{3}\times\mathbb{R}$ space-time. We then derive the analytic solutions of spin density, spin potential and other thermodynamic in $dS_{3}\times\mathbb{R}$ space-time and transform them back into Minkowski space-time $\mathbb{R}^{3,1}$. In the Minkowski space-time, the spin density and spin potential including the information of radial expansion decay as $\sim L^{-2}\tau^{-1}$ and $\sim L^{-2}\tau^{-1/3}$ in large $L$ limit, with $\tau$ being proper time and $L$ being the characteristic length of the system, respectively. Moreover, we observe the non-vanishing spin corrections to the energy density and other dissipative terms in the Belinfante form of dissipative spin hydrodynamics. Our results can also be used as test beds for future simulations of relativistic dissipative spin hydrodynamics.