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Instability of closed spaces in general relativity

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Abstract

There are strong restrictions on the solutions of the initial value constraints of General Relativity when the spatial hypersurface is closed. In particular, closed flat space is unstable: not all solutions of the linearized constraints correspond to nearby solutions of the constraints themselves. For example, no nearby solutions whatever exist which are time symmetric. Other restrictions, which limit perturbations of non-flat closed initial solutions, are also exhibited.

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References

  1. Nowacki, W.: Commentarii Mathematici Helvetici7, 81 (1935).

    Google Scholar 

  2. Choquet-Bruhat, Y., Deser, S.: On Stability of Flat Space, Ann. Phys. (N. Y.) (to appear 1973).

  3. Arnowitt, R., Deser, S., Misner, C.: Phys. Rev.122, 997 (1961).

    Google Scholar 

  4. Brill, D., Deser, S.: Ann. Phys. (N. Y.)50, 548 (1968).

    Google Scholar 

  5. Deser, S.: Ann. Inst. H. Poincaré7, 149 (1967).

    Google Scholar 

  6. Brill, D.: Isolated Solutions in General Relativity, in Gravitation: Problems and Prospects, Naukova Dumka (Kiev 1972), p. 17.

  7. York, J.: J. Math. Phys.14, 456 (1973).

    Google Scholar 

  8. Wald, R., Geroch, R.: unpublished.

  9. Kasner, E.: Am. Jour. Math.43, 217 (1921).

    Google Scholar 

  10. Gowdy, R. H.: Phys. Rev. Letters27, 826 (1971).

    Google Scholar 

  11. Taub, A. H.: Ann. Math.53, 472 (1951).

    Google Scholar 

  12. Fischer, A. E., Marsden, J. E.: Linearization Stability of the Einstein Equations. Bull. Am. Math. Soc., September 1973

  13. Choquet-Bruhat, Y.: Commun. math. Phys.21, 211 (1971).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Max Planck Institute for Physics and Astrophysics, Munich, Germany

    Dieter R. Brill

  2. Department of Physics and Astronomy, University of Maryland, College Park, Md., USA

    Dieter R. Brill

  3. Laboratoire de Physique Théorique et Hautes Energies, Orsay, France

    Stanley Deser

  4. Physics Department, Brandeis University, Waltham, Mass., USA

    Stanley Deser

Authors
  1. Dieter R. Brill
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  2. Stanley Deser
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Additional information

Supported in part by the National Science Foundation and by the Humboldt-Foundation.

Supported in part by Grant AFOSR 70-1864.

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Brill, D.R., Deser, S. Instability of closed spaces in general relativity. Commun.Math. Phys. 32, 291–304 (1973). https://doi.org/10.1007/BF01645610

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  • DOI: https://doi.org/10.1007/BF01645610

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