Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

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.

arXiv commentThis is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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• Exact (1+1)-dimensional flows of a perfect fluid
• Scalar field vs hydrodynamic models in the homogeneous isotropic cosmology