Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics

TL;DR

This paper introduces a new family of exact, accelerating solutions to relativistic perfect fluid hydrodynamics, improving realism over previous models and aiding in the analysis of high-energy heavy ion collisions.

Contribution

It presents a generalized ansatz extending the Hwa-Bjorken solution, providing explicit accelerating solutions that better model collision dynamics and enable more accurate initial condition estimations.

Findings

New class of exact accelerating solutions for relativistic hydrodynamics

More realistic initial energy density estimates in heavy ion collisions

Stable solutions with arbitrary initial pressure and velocity profiles

Abstract

In this paper we describe in full details a new family of recently found exact solutions of relativistic, perfect fluid dynamics. With an ansatz, which generalizes the well-known Hwa-Bjorken solution, we obtain a wide class of new exact, explicit and simple solutions, which have a remarkable advantage as compared to presently known exact and explicit solutions: they do not lack acceleration. They can be utilized for the description of the evolution of the matter created in high energy heavy ion collisions. Because these solutions are accelerating, they provide a more realistic picture than the well-known Hwa-Bjorken solution, and give more insight into the dynamics of the matter. We exploit this by giving an advanced simple estimation of the initial energy density of the produced matter in high energy collisions, which takes acceleration effects (i.e. the work done by the pressure and the modified change of the volume elements) into account. We also give an advanced estimation of the life-time of the reaction. Our new solutions can also be used to test numerical hydrodynamical codes reliably. In the end, we also give an exact, 1+1 dimensional, relativistic hydrodynamical solution, where the initial pressure and velocity profile is arbitrary, and we show that this general solution is stable for perturbations.