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

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 $d{S}_3\times \mathbb{R}$ space-time. We then derive the analytic solutions of spin density, spin potential and other thermodynamic in $d{S}_3\times \mathbb{R}$ 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.

28 pages; 1 table and 1 figure are added

References in corpus (28)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Angular momentum conservation in heavy ion collisions at very high energy
• Lorentz Invariance in Chiral Kinetic Theory
• Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy
• Global quark polarization in non-central $A+A$ collisions
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Entropy Current in Conformal Hydrodynamics
• Collisions in Chiral Kinetic Theory
• Global $\Lambda$ Polarization in high energy collisions
• Global polarization measurement in Au+Au collisions
• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• Lambda hyperon polarization in relativistic heavy ion collisions from the chiral kinetic approach
• Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory
• The ideal relativistic spinning gas: polarization and spectra
• Large rotating AdS black holes from fluid mechanics
• Mass Correction to Chiral Kinetic Equations
• A hydrodynamic study of hyperon spin polarization in relativistic heavy ion collisions
• Spin polarization evolution in a boost invariant hydrodynamical background
• Analytical and numerical Gubser solutions of the second-order hydrodynamics
• Anisotropic hydrodynamics for conformal Gubser flow
• Anomalous magnetohydrodynamics with longitudinal boost invariance and chiral magnetic effect
• Spin polarization dynamics in the non-boost-invariant background
• Hydrodynamic helicity polarization in relativistic heavy ion collisions
• Kinetic theory with spin: From massive to massless fermions
• Evolution of $\Lambda$ polarization in the hadronic phase of heavy-ion collisions
• Vorticity and $\Lambda$ polarization in the microscopic transport model PACIAE
• Massless Limit of Transport Theory for Massive Fermions
• Polarization in low energy kaon-hyperon interaction

Cited by in corpus (16)

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• Foundations and Applications of Quantum Kinetic Theory
• Relativistic Spin Magnetohydrodynamics
• Lorentz-covariant nonlocal collision term for spin-1/2 particles
• Damping of spin waves
• Resummed spin hydrodynamics from quantum kinetic theory
• Spin dynamics with realistic hydrodynamic background for relativistic heavy-ion collisions
• Anomalous magnetohydrodynamics with temperature-dependent electric conductivity and application to the global polarization
• An introduction to relativistic spin hydrodynamics
• Cross effects in spin hydrodynamics: A revisit Entropy analysis and statistical operator
• Collisional corrections to spin polarization from quantum kinetic theory using Chapman-Enskog expansion
• Relativistic second-order spin hydrodynamics: A Kubo-type formulation for the quark-gluon plasma
• Collective dynamics of polarized spin-half fermions in relativistic heavy-ion collisions
• Thermal dilepton production within conformal viscous Gubser flow
• Semi-Classical Spin Hydrodynamics in Flat and Curved Spacetime: Covariance, Linear Waves, and Bjorken Background
• Finite-Density Dynamics of Chemically Equilibrating QGP in Conformal Gubser Flow and Hard Thermal Photon Production