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The Weyl tensor and equilibrium configurations of self-gravitating fluids. (English) Zbl 1016.83026
Summary: It is shown that (except for two well defined cases), the necessary and sufficient condition for any spherically symmetric distribution of fluid to leave the state of equilibrium (or quasi-equilibrium), is that the Weyl tensor changes with respect to its value in the state of equilibrium (or quasi-equilibrium).

MSC:
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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