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

TL;DR

This paper introduces a novel method for solving (1+3)D relativistic ideal hydrodynamics with embedded longitudinal and transverse flows, simplifying the equations to a single transverse velocity equation and deriving all power-law solutions.

Contribution

The paper presents a new approach that reduces complex hydrodynamic equations to a single manageable equation, enabling analytical solutions with power-law dependencies.

Findings

Derived all power-law solutions for the transverse velocity field.

Reduced hydrodynamic equations to a single tractable equation.

Discussed applications to relativistic heavy ion collisions.

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.