Exact Relativistic Ideal Hydrodynamical Solutions in (1+3)D with Longitudinal and Transverse Flows

Abstract

A new method for solving relativistic ideal hydrodynamics in (1+3)D is developed. Longitudinal and transverse radial flows are explicitly embedded and the hydrodynamic equations are reduced to a single equation for the transverse velocity field only, which is much more tractable. As an application we use the method to find analytically all possible solutions with power dependence on proper time and transverse radius. Possible application to the Relativistic Heavy Ion Collisions and possible generalizations of the method are discussed.