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Static uniform-density stars must be spherical in general relativity. (English) Zbl 0641.76139

Summary: In this paper the uniqueness of the static solutions of Einstein’s equation that represent isolated uniform-density perfect-fluid stellar models is demonstrated: any static asymptotically flat space-time containing only a uniform-density perfect fluid confined to a spatially compact world tube is necessarily spherically symmetric. This result generalizes to relativistic uniformdensity models the well known Newtonian theorem of Carleman and Lichtenstein.

MSC:

76Y05 Quantum hydrodynamics and relativistic hydrodynamics
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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