Transverse expansion of hot magnetized Bjorken flow in heavy ion collisions

We argue that the existence of an inhomogeneous external magnetic eld can lead to radial flow in transverse plane. Our aim is to show how the introduction of a magnetic eld generalizes the Bjorken flow. We investigate the eect of an inhomogeneous weak external magnetic eld on the transverse expansion of in-viscid fluid created in high energy nuclear collisions. In order to simplify our calculation and compare with Gubser model, we consider the fluid under investigation to be produced in central collisions, at small impact parameter; azimuthal symmetry has been considered. In our model, we assume an inhomogeneous external magnetic eld following the power-law decay in proper time and having radial inhomogeneity perpendicular to the radial velocity of the in-viscid fluid in the transverse plane; then the space time evolution of the transverse expansion of the fluid is obtained. We also show how the existence of an inhomogeneous external magnetic eld modies the energy density. Finally we use the solutions for the transverse velocity and energy density in the presence of a weak magnetic eld, to estimate the transverse momentum spectrum of protons and pions emerging from the Magneto-hydrodynamic solutions.