Transverse and non-boost longitudinal expansion of (2+1)dimensional relativistic ideal-hydrodynamics flow in heavy ion collisions

Abstract: This study investigates the evolution of quark gluon plasma (QGP) within a generalized Bjorken flow framework. The medium under consideration is assumed to possess a finite transverse size and to expand both radially and along the beam axis. However, we assume that the boost invariance of longitudinal expansion is broken. To be more specific, we generalize the Bjorken solution to include the acceleration and transverse expansion of the fluid. We analytically study the (2 + 1) dimensional longitudinal acceleration expansion of hot and dense quark matter, applying a perturbation approach to solve the relativistic hydrodynamics equations. This procedure enables us to obtain exact algebraic expressions for fluid velocities and energy densities in both transverse and longitudinal directions. To simplify our calculations, we assume that the fluid is produced in central collisions, and therefore, we consider azimuthal symmetry. We compare the radial velocity and correction energy density with those obtained from the Gubser model. Furthermore, we determine the fluid's acceleration parameter and longitudinal correction energy density, which exhibits a Gaussian distribution.