1+1 dimensional relativistic viscous non-resistive magnetohydrodynamics with longitudinal boost invariance

We study 1+1 dimensional relativistic non-resistive magnetohydrodynamics (MHD) with longitudinal boost invariance and shear stress tensor. Several analytical solutions that describe the fluid temperature evolution under the equation of state (EoS) \(\varepsilon=3p\) are derived, relevant to relativi...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Ze-Fang Jiang, Shuo-Yan Liu, Tian-Yu, Hu, Huang-Jing, Zheng, Duan She
Format: Article
Language:English
Subjects:
Cooling rate
Equations of state
Exact solutions
Heavy ions
Invariance
Ionic collisions
Magnetic fields
Magnetohydrodynamic flow
Magnetohydrodynamics
Mathematical analysis
Relativistic effects
Shear stress
Shear viscosity
Tensors
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Summary:We study 1+1 dimensional relativistic non-resistive magnetohydrodynamics (MHD) with longitudinal boost invariance and shear stress tensor. Several analytical solutions that describe the fluid temperature evolution under the equation of state (EoS) \(\varepsilon=3p\) are derived, relevant to relativistic heavy-ion collisions. Extending the Victor-Bjorken ideal MHD flow to include non-zero shear viscosity, two perturbative analytical solutions for the first-order (Navier-Stokes) approximation are obtained. For small, power-law evolving external magnetic fields, our solutions are stable and show that both magnetic field and shear viscosity cause fluid heating with an early temperature peak, align with the numerical results. In the second-order (Israel-Stewart) theory, our findings show that the combined presence of magnetic field and shear viscosity leads to a slow cooling rate of fluid temperature, with initial shear stress significantly affecting temperature evolution of QGP.
ISSN:2331-8422