A Symmetric Hyperbolic Structure for Isentropic Relativistic Perfect Fluids

• Autores: Ronald A. Walton
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 1, 2005, págs. 145-160
• Idioma: inglés
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• Resumen

  • The dependent variables of an isentropic, relativistic perfect fluid can be consolidated into a generalized velocity vector field equal to the fluid's relativistic velocity vector field divided pointwise by the value of the fluid's specific enthalpy. The equations of motion for an isentropic, relativistic perfect fluid then become a quasilinear, first order, symmetric system of partial differential equations, equivalent to local energy and momentum conservation in the fluid. Furthermore, these equations of motion are symmetric hyperbolic wherever the material density of the fluid is positive and the speed of sound in the fluid does not exceed the speed of light. Two applications of these equations are presented. First, the characteristic hypersurfaces of an isentropic, relativistic perfect fluid are proven to consist of (1) timelike hypersurfaces generated by the fluid streamlines and (2) nonspacelike, conical hypersurfaces defined by the propagation of sound waves. And second, the equations of motion for a self-gravitating, isentropic, relativistic perfect fluid are proven to be equivalent to a quasilinear, first order, symmetric hyperbolic system if the spacetime coordinates are constrained to be harmonic.