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.


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


[1] DOI: 10.1007/BF01292592
[2] DOI: 10.1007/BF01210611 · Zbl 0612.53042
[3] Avez A., C. R. Acad. Sci. Paris 257 pp 3316– (1963)
[4] Avez A., Ann. Inst. H. PoincarĂ© A 1 pp 291– (1964)
[5] DOI: 10.1007/BF01646528
[6] DOI: 10.1063/1.524573
[7] DOI: 10.1063/1.525028
[8] DOI: 10.1007/BF00756470 · Zbl 0546.53048
[9] DOI: 10.1088/0264-9381/4/3/020 · Zbl 0613.53038
[10] DOI: 10.1007/BF01940959 · Zbl 0405.53045
[11] DOI: 10.1007/BF01208277 · Zbl 1051.83532
[12] DOI: 10.1002/cpa.3160390505 · Zbl 0598.53045
[13] DOI: 10.1007/BF00756175 · Zbl 0454.35083
[14] DOI: 10.1007/BF00756322 · Zbl 0429.53043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.