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Vorticity and isotropic singularities

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Abstract

We prove that if a solution of the Einstein field equations with perfect fluid source and γ law equation of state [p = (γ−1)μ] admits an Isotropic singularity, then necessarily the fluid flow is irrotational. This shows the essential equivalence of the seemingly distinct concepts of quasi-isotropic singularities and Friedrnann-like singularities of Lifshitz and Khalatnikov and Eardley, Liang and Sachs, respectively.

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References

  1. MacCalium, M. A. H. (1979). In Hawking, S. W., and Israel, W. (eds.),General Relativity, An Einstein Centenary (Cambridge University Press, Cambridge).

    Google Scholar 

  2. Barrow, J. D. (1978).Nature,272, 211–215.

    Google Scholar 

  3. Barrow, J. D., and Matzner, R. A. (1977).Mon. Not. R. Astr. Soc.,181, 719–727.

    Google Scholar 

  4. Aly, J. J. (1979).Mon. Not. R. Astr. Soc.,189, 479–482.

    Google Scholar 

  5. Penrose, R. (1979). In Hawking, S. W., and Israel, W. (eds.),General Relativity, An Einstein Centenary (Cambridge University Press, Cambridge).

    Google Scholar 

  6. Wainwright, J., and Anderson, P. J. (1984).Gen. Rel. Grav.,16, 610–624.

    Google Scholar 

  7. Goode, S. W., and Wainwright, J. (1985).Class. Quantum Grav.,2, 99–115.

    Google Scholar 

  8. Lifshitz, E. M., and Khalatnikov, I. M. (1963).Adv. Phys.,12, 185–249.

    Google Scholar 

  9. Eardley, D., Liang, E., and Sachs, R. K. (1972).J. Math. Phys.,13, 99–106.

    Google Scholar 

  10. Liang, E. P. T. (1972).J. Math. Phys.,13, 386–393.

    Google Scholar 

  11. Ellis, G. F. R. (1973). In Schatzman, E. (ed.).Cargese Lectures in Physics 6. Lectures at International Summer School of Physics, Cargese, Corsica, 1971 (Gordon and Breach, New York).

    Google Scholar 

  12. Ehlers, J. (1961).Akad. Wiss. Lit. Mainz Nat. Kl.,11, 793–837.

    Google Scholar 

  13. Kramer, D., Stephani, H., Herlt, E., and MacCallum, M. A. H. (1980).Exact Solutions of the Einstein Field Equations (Cambridge University Press, Cambridge).

    Google Scholar 

  14. Goode, S. W. (1983). Spatially Inhomogeneous Cosmologies and their Relation with the Friedmann-Robertson-Walker Models,PhD Thesis (University of Waterloo).

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  1. Department of Mathematics, California State University, 92634, Fullerton, Fullerton, California, USA

    Stephen W. Goode

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  1. Stephen W. Goode
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Goode, S.W. Vorticity and isotropic singularities. Gen Relat Gravit 19, 1075–1082 (1987). https://doi.org/10.1007/BF00759143

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