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General Relativistic Hydrodynamics

In: Hyperbolic Equations and Waves

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  • A. H. Taub

Abstract

The material covered in the lecture given under this title is contained in the papers: “Relativistic Hydrodynamics” reprinted from the American Mathematical Society’s Lectures in Applied Mathematics, Volume 81 and “Stability of Fluid Motions and Variational Principles”, a paper presented at the International Colloque de Fluid Mechanique et Gravitation in Paris, June 19672. In the first paper the equations of motion for special relativistic hydrodynamics are derived from a Lorentz invariant formulation of the Boltzmann equation and various properties of the solution of these equations which hold for an arbitrary space-time are discussed. The Einstein field whose source is a fluid mass are described. Three methods of dealing equations for a gravitationed field: (1) The determination of field equations involving the metric alone from the algebraic properties of the fluid stress energy tensor. (2) The supplementation of the field equations by the conservation of particle number. (3) The supplementation of the field equation by an equation of state, that is by the requirement that the pressure p be a function of the energy density W alone, (or by an equivalent statement).

Suggested Citation

  • A. H. Taub, 1970. "General Relativistic Hydrodynamics," Springer Books, in: M. Froissart (ed.), Hyperbolic Equations and Waves, pages 22-23, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-87025-5_6
    DOI: 10.1007/978-3-642-87025-5_6
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