Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

TL;DR

This paper derives exact analytic solutions for non-stationary inhomogeneous relativistic perfect fluid flows using a connection to scalar field theory, covering various symmetries and equations of state.

Contribution

It introduces a method to generate exact solutions for relativistic hydrodynamics with different equations of state, including self-similar and axially symmetric solutions.

Findings

Derived self-similar solutions for linear EOS with various symmetries

Obtained axially symmetric solutions for stiff EOS ($a=1$)

Identified nonlinear EOSs admitting analytic solutions

Abstract

We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of the perfect fluid with one-parametric equation of state (EOS) $p = p(\epsilon)$. For linear EOS $p = \kappa \epsilon$ we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS ($\kappa=1$) we obtain ''monopole + dipole'' and ''monopole + quadrupole'' axially symmetric solutions. We also found some nonlinear EOSs that admit analytic solutions.