Stability of Fluid Motions and Variational Principles

  • A. H. Taub

Abstract

It is the purpose of this paper to show that the equations satisfied by the difference of two “nearly equal” solutions of the Einstein field equations are derivable from a variational principle and indicate how this principle may be used to study the time dependence of the difference. The source of the gravitational fields will be assumed to be a perfect fluid obeying an equation of state. That is, the pressure p of the fluid will be assumed to be a function of only the energy density w. It will be further assumed that the perturbations in the fluid motions will be adiabatic. That is if the entropy for one solution is S and that for the nearby solution is S + e S′ then S′ = 0. It will not be assumed that S = constant for either solution although this condition does provide one of the possible equations of state that the fluid is required to obey.

Keywords

Entropy Vorticity Cali 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Taub, A. H.: General relativistic variational principle for perfect fluids. Phys. Rev. 94, 1468–1470 (1954).MathSciNetCrossRefGoogle Scholar
  2. 2.
    Taub, A. H.: Singular Hypersurfaces in General Relativity. Illinois Journal of Mathematics 1, 370–388 (1957).MathSciNetMATHGoogle Scholar
  3. 3.
    Taub, A. H.: Approximate Stress Energy Tensor for Gravitational Fields. Journ. Math. Phys. 2, 787–793 (1961).MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Capella, A.: Thèse. Université de Paris (1963).Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1970

Authors and Affiliations

  • A. H. Taub

There are no affiliations available

Personalised recommendations