On the Equilibrium Figures of an Ideal Rotating Fluid in the PostNewtonian Approximation of General Relativity. III: Stability of the Forms of Equilibrium
Abstract
A stability criterion is given for the equilibrium form of an ideal rotating fluid in the postNewtonian 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).
 Publication:

Astrophysics and Space Science
 Pub Date:
 March 1975
 DOI:
 10.1007/BF00646009
 Bibcode:
 1975Ap&SS..33...75P
 Keywords:

 Dynamic Stability;
 Ideal Fluids;
 Liapunov Functions;
 Mathematical Models;
 Relativity;
 Rotating Fluids;
 Angular Velocity;
 Equilibrium;
 Gravitation Theory;
 Lagrangian Equilibrium Points;
 Rotating Spheres;
 Schwarzschild Metric;
 Astrophysics