Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

• Published in: Symmetry, integrability and geometry, methods and applications Vol. 3; p. 116
• Main Author: Borshch, Maxim S.
• Format: Journal Article
• Language: English
• Published: Kiev National Academy of Sciences of Ukraine 01-01-2007; National Academy of Science of Ukraine
• Subjects: exact solutions; relativistic hydrodynamics
• ISSN: 1815-0659; 1815-0659
• DOI: 10.3842/SIGMA.2007.116

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(?). For linear EOS p = ?? we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS (? = 1) we obtain ''monopole + dipole'' and ''monopole + quadrupole'' axially symmetric solutions. We also found some nonlinear EOSs that admit analytic solutions.