Causality and stability in relativistic viscous non-resistive magneto-fluid dynamics

Rajesh Biswas,Shi Pu,Ashutosh Dash,Victor Roy,Najmul Haque

doi:10.1007/jhep10(2020)171

Abstract

We investigate the causality and the stability of the relativistic viscous non-resistive magneto-hydrodynamics in the framework of the Israel-Stewart (IS) second-order theory, and also within a modified IS theory which incorporates the effect of magnetic fields in the relaxation equations of the viscous stress. We compute the dispersion relation by perturbing the fluid variables around their equilibrium values. In the ideal magnetohydrodynamics limit, the linear dispersion relation yields the well-known propagating modes: the Alfvén and the magneto-sonic modes. In the presence of bulk viscous pressure, the causality bound is found to be independent of the magnitude of the magnetic field. The same bound also remains true, when we take the full non-linear form of the equation using the method of characteristics. In the presence of shear viscous pressure, the causality bound is independent of the magnitude of the magnetic field for the two magneto-sonic modes. The causality bound for the shear-Alfvén modes, however, depends both on the magnitude and the direction of the propagation. For modified IS theory in the presence of shear viscosity, new non-hydrodynamic modes emerge but the asymptotic causality condition is the same as that of IS. In summary, although the magnetic field does influence the wave propagation in the fluid, the study of the stability and asymptotic causality conditions in the fluid rest frame shows that the fluid remains stable and causal given that they obey certain asymptotic causality condition.

Highlights

Simualations based on this framework can be found in refs. [32,33,34,35,36,37,38,39]
We investigate the causality and the stability of the relativistic viscous nonresistive magneto-hydrodynamics in the framework of the Israel-Stewart (IS) second-order theory, and within a modified IS theory which incorporates the effect of magnetic fields in the relaxation equations of the viscous stress
It is natural to expect that the appropriate equation of motion of the high temperature QGP and low temperature hadronic phase under large magnetic fields is given by the relativistic viscous magneto-hydrodynamic framework

Summary

Introduction

Simualations based on this framework can be found in refs. [32,33,34,35,36,37,38,39]. [52, 53] relativistic Boltzmann equation was used to study the effect of electromagnetic fields in heavy-ion collisions. It is widely accepted that the QGP produced in high energy heavy-ion collisions behaves as almost ideal fluid (i.e., possess very small shear and bulk viscosity) This conclusion was made primarily based on the success of relativistic viscous hydrodynamics simulations in explaining a multitude of experimental data with a very small specific shear viscosity (η/s) as an input refs. Relativistic magnetohydrodynamics (RMHD) is a self-consistent macroscopic framework which describe the evolution of any charged fluid in the presence of electromagnetic fields refs. We have derived the analytic solutions of MHD in the presence of finite electric conductivity, CME and chiral anomaly ref. For numerical simulations of ideal MHD, one can see refs. [104, 105]

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