A global analysis approach to the general relativistic fluid ball problem
This paper studies the conjecture that the Einstein equations require that every bounded, static, perfect fluid solution in otherwise empty, asymptotically flat space, is necessarily spherically symmetric. Physical intuition strongly supports this conjecture, which is easily shown to be true for Newtonian gravity. A weakened form of this conjecture is established in this paper: If a family of static perfect fluid solutions of fixed total mass depends differentiably on one parameter and contains the spherically symmetric one, then every member of the family is diffeomorphic (and thus physically equivalent) to it. The global methods of \textit{A. E. Fischer} and \textit{J. E. Marsden} are used [Differ. Geom., Proc. Symp. Pure Math. 27, Part 2, 219-263 (1975; Zbl 0314.53031) and Duke Math. J. 42, 519-547 (1975; Zbl 0336.53032)].
scientific article; zbMATH DE number 3870164