In the initial stage of relativistic heavy-ion collisions, strong magnetic fields appear due to the large velocity of the colliding charges. The evolution of these fields appears as a novel and intriguing feature in the fluid-dynamical description of heavy-ion collisions. In this work, we study analytically the one-dimensional, longitudinally boost-invariant motion of an ideal fluid in the presence of a transverse magnetic field. Interestingly, we find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite conductivity, and irrespective of the strength of the initial magnetization, the decay of the fluid energy density e with proper time τ is the same as for the time-honoured “Bjorken flow” without magnetic field. Furthermore, when the magnetic field is assumed to decay ∼τ−a, where a is an arbitrary number, two classes of analytic solutions can be found depending on whether a is larger or smaller than one. In summary, the analytic solutions presented here highlight that the Bjorken flow is far more general than formerly thought. These solutions can serve both to gain insight on the dynamics of heavy-ion collisions in the presence of strong magnetic fields and as testbeds for numerical codes

An intense transient magnetic field is produced in high energy heavy-ion collisions mostly due to the spectator protons inside the two colliding nuclei. The magnetic field introduces anisotropy in the medium, and hence the isotropic scalar transport coefficients become anisotropic and split into multiple components. Here, we calculate the anisotropic transport coefficients’ shear, bulk viscosity, and electrical conductivity, and the thermal diffusion coefficients for a multicomponent hadron resonance gas (HRG) model for a nonzero magnetic field by using the Boltzmann transport equation in a relaxation time approximation (RTA). The anisotropic transport coefficient component along the magnetic field remains unaffected by the magnetic field, while perpendicular dissipation is governed by the interplay of the collisional relaxation time and the magnetic time scale, which is inverse of the cyclotron frequency. We calculate the anisotropic transport coefficients as a function of temperature and magnetic field using the HRG model. The neutral hadrons are unaffected by the Lorentz force and do not contribute to the anisotropic transports, we estimate within the HRG model the relative contribution of isotropic and anisotropic transports as a function of magnetic field and temperature. We also give an estimation of these anisotropic transport coefficients for the hadronic gas at finite baryon chemical potential (${\mu }_B$).

We derive the relativistic non-resistive, viscous second-order magnetohydrodynamic equations for the dissipative quantities using the relaxation time approximation. The Boltzmann equation is solved for a system of particles and antiparticles using Chapman-Enskog like gradient expansion of the single-particle distribution function truncated at second order. In the first order, the transport coefficients are independent of the magnetic field. In the second-order, new transport coefficients that couple magnetic field and the dissipative quantities appear which are different from those obtained in the 14-moment approximation [1] in the presence of a magnetic field. However, in the limit of the weak magnetic field, the form of these equations are identical to the 14-moment approximation albeit with different values of these coefficients. We also derive the anisotropic transport coefficients in the Navier-Stokes limit.

Here we derive the relativistic resistive dissipative second-order magnetohydrodynamic evolution equations using the Boltzmann equation, thus extending our work from the previous paper [A. K. Panda et al., J. High Energy Phys. 03 (2021) 216] where we considered the nonresistive limit. We solve the Boltzmann equation for a system of particles and antiparticles using the relaxation time approximation and the Chapman-Enskog–like gradient expansion for the off-equilibrium distribution function, truncating beyond second order. In the first order, the bulk and shear stress are independent of the electromagnetic field, however, the diffusion current shows a dependence on the electric field. In the second order, the new transport coefficients that couple electromagnetic fields with the dissipative quantities appear, which are different from those obtained in the 14-moment approximation [G. S. Denicol et al., Phys. Rev. D 99, 056017 (2019).] in the presence of the electromagnetic field. Also, we found the various components of conductivity in this case.