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On the spherical symmetry of a static perfect fluid

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Abstract

A globally static space-time with asymptotically Euclidean behavior representing a finite body of a perfect fluid and a vacuum region is shown to be diffeomorphic to Euclidean space and its metric spherically symmetric whenever the magnitude of the gravitational field strength is only a function of the gravitational potential. Under some additional physical assumptions it is then proved that this spherically symmetric solution is not deformable, that is, does not admit a nontrivial first order perturbation that is also a static, asymptotically Euclidean perfect fluid with the same equation of state and the same central value of the pressure and the gravitational potential.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, California

    H. P. Künzle

  2. Department of Mathematics, University of Alberta, Edmonton 7, Alberta, Canada

    H. P. Künzle

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  1. H. P. Künzle
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Additional information

This work was supported in part by the United States Atomic Energy Commission under contract number AT (04-3)-34, Project Agreement No. 125.

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Künzle, H.P. On the spherical symmetry of a static perfect fluid. Commun.Math. Phys. 20, 85–100 (1971). https://doi.org/10.1007/BF01646528

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  • DOI: https://doi.org/10.1007/BF01646528

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