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On the equilibrium figures of an ideal rotating fluid in the post-newtonian approximation of general relativity

III: Stability of the forms of equilibrium

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Abstract

A stability criterion is given for the equilibrium form of an ideal rotating fluid in the post-Newtonian approximation. This generalizes the known Lyapunov criterion in classical dynamics. The sphere stability is also investigated and it is shown that it is stable only whenR>22.2R g (R is the relativistic sphere radius,R g the Schwarzschild radius).

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Authors and Affiliations

  1. Institute for Theoretical Physics, Kiev, U.S.S.R.

    K. A. Pyragas & N. P. Bondarenko

  2. Institute of Mathematics, Kiev, U.S.S.R.

    A. N. Kryshtal

Authors
  1. K. A. Pyragas
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  2. N. P. Bondarenko
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  3. A. N. Kryshtal
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Pyragas, K.A., Bondarenko, N.P. & Kryshtal, A.N. On the equilibrium figures of an ideal rotating fluid in the post-newtonian approximation of general relativity. Astrophys Space Sci 33, 75–97 (1975). https://doi.org/10.1007/BF00646009

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  • DOI: https://doi.org/10.1007/BF00646009

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