Theoretical test of an axiom of general relativity. (Test théorique d’un axiome de la relativité générale.) (French) Zbl 0918.53035

Séminaire de théorie spectrale et géométrie. Année 1993-1994. Chambéry: Univ. de Savoie, Fac. des Sciences, Service de Math. Sémin. Théor. Spectrale Géom., Chambéry-Grenoble. 12, 11-18 (1994).
The present paper is an overview and survey of the author’s work on the problem of the liquid ball in general relativity. This appears to be the following question: “Given a stationary globule of perfect fluid in an asymptotically flat curved spacetime, under what conditions does the globule have exact spherical symmetry?” The author argues that the answer is related to the classical compatibility conditions of A. Lichnerowicz [(‘Théories relativistes de la gravitation et de l’électromagnétisme’ (Masson et Cie, Paris) (1955; Zbl 0065.20704)], or equivalently the conditions of S. O’Brien and J. L. Synge [‘Jump conditions at discontinuities in general relativity’, Commun. Dublin Inst. Advanced Stud., Ser. A 9 (1952; Zbl 0047.20802)], and it is indicated how the imposition of these conditions is related to various topological results of H. Poincaré (on the indices of singularity of a vector field), and a theorem of H. Whitney (on the replacement of smoothness by real-analyticity on a differentiable manifold). In other words, a seemingly simple physical result in general relativity has nontrivial consequences on the mathematical structure of the spacetime, and presumably this is what is meant by the somewhat mysterious title of the paper.
Unfortunately, the author offers us only a glimpse of his reasoning, and at the time of publication his preliminary work on the problem of the liquid ball was available only in peprint form as Preprint 266 of L’Institut Fourier. Hopefully, these results have now been formally published.
For the entire collection see [Zbl 0812.00007].


53Z05 Applications of differential geometry to physics
83C99 General relativity
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