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

TL;DR

This paper derives analytical solutions for 1+1D relativistic viscous non-resistive MHD with boost invariance, revealing how magnetic fields and shear viscosity influence temperature evolution in quark-gluon plasma.

Contribution

It extends ideal MHD solutions to include shear viscosity and provides perturbative analytical solutions under various conditions, advancing understanding of QGP dynamics.

Findings

Magnetic field and shear viscosity cause early fluid heating.

Solutions are stable for small, power-law magnetic fields.

Magnetic field and viscosity slow down cooling in QGP.

Abstract

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.