Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

Understand

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.