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A global analysis approach to the general relativistic fluid ball problem

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Abstract

That a self-gravitating perfect fluid in empty space has a spherical equilibrium configuration if it is static-i.e., nonrotating-is considered physically evident, but has not yet been rigorously derived from Einstein's field equations together with suitable asymptotic conditions. In this paper the global analysis techniques developed recently mainly by Fischer, Marsden, and Cantor are used to derive the result that if a family of static perfect fluid solutions with fixed total gravitational massm and fixed equation of stateϱ(p) satisfying 0 ⩽p ⩽ ϱ and 0 ⩽dϱ/dp < ∞ depends differentiably on a parameter and contains the spherically symmetric solution then it must consist of solutions diffeomorphic to the spherically symmetric one.

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Authors and Affiliations

  1. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Alberta, Canada

    H. P. Künzle

  2. Department of Physics, University of Alberta, T6G 2 J1, Edmonton, Alberta, Canada

    J. R. Savage

Authors
  1. H. P. Künzle
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  2. J. R. Savage
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Partially supported by the National Sciences and Engineering Research Council, grant No. A8059.

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Künzle, H.P., Savage, J.R. A global analysis approach to the general relativistic fluid ball problem. Gen Relat Gravit 12, 155–174 (1980). https://doi.org/10.1007/BF00756470

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