# 1+1 dimensional relativistic magnetohydrodynamics with longitudinal acceleration

## TL;DR

This paper explores how longitudinal acceleration and magnetic fields influence the evolution of energy density and temperature in 1+1 dimensional relativistic magnetohydrodynamics relevant to heavy-ion collisions.

## Contribution

It introduces a detailed analysis of the effects of longitudinal acceleration, magnetic field decay, and initial magnetization on relativistic MHD in heavy-ion collision scenarios.

## Key findings

- Longitudinal acceleration significantly affects energy density evolution.
- Magnetic field decay impacts temperature dynamics.
- Initial magnetization alters the system's energy density trajectory.

## Abstract

Non-central heavy-ion collisions generate the strongest magnetic field of the order of $10^{18}-10^{19}$ Gauss due to the electric current produced by the positively charged spectators that travel at nearly the speed of light. Such transient electromagnetic fields may induce various novel effects in the hydrodynamic description of the quark gluon plasma for non-central heavy-ion collisions. We investigate the longitudinal acceleration effects on the 1+1 dimensional relativistic magnetohydrodynamics with transverse magnetic fields. We analyze the proper time evolution of the system energy density. We find that the longitudinal acceleration parameter $\lambda^*$, magnetic field decay parameter $a$, equation of state $\kappa$, and initial magnetization $\sigma_0$ have nontrivial effects on the evolutions of the system energy density and temperature.