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Extensions of the Taub and NUT spaces and extensions of their tangent bundles

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Abstract

A system of extensions of the Taub space and the NUT space with the topology due to Misner is constructed having the property: for each incomplete geodesic in these space-times, there is one and only one extension from the system into which the geodesic smoothly continues. Next, the notion of hypermanifold is introduced which is a generalization of tangent bundle of a space-time, and an untrivial hypermanifold is constructed that contains the tangent bundles of the Taub and NUT spaces as proper submanifolds, and within which almost all geodesics are complete. Locally, the hypermanifolds do not yield anything new, but they provide much broader choice of global properties than any four-dimensional space-time manifold.

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References

  1. Carter, B.: Phys. Rev.174, 1559 (1968).

    Google Scholar 

  2. Penrose, R.: Phys. Rev. Letters14, 57 (1965).

    Google Scholar 

  3. Hawking, S. W.: Proc. Roy. Soc. A,294, 511 (1966).

    Google Scholar 

  4. —— Proc. Roy. Soc. A,295, 490 (1966).

    Google Scholar 

  5. —— Proc. Roy. Soc. A,300, 187 (1967).

    Google Scholar 

  6. Geroch, R. P.: Phys. Rev. Letters17, 446 (1966).

    Google Scholar 

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

    Google Scholar 

  8. Newman, E., Tamburino, L., Unti, T.: J. Math. Phys.4, 915 (1963).

    Google Scholar 

  9. Misner, C. W.: J. Math. Phys.4, 924 (1963).

    Google Scholar 

  10. Bonnor, W. B.: Proc. Cambridge Phil. Soc.66, 145 (1969).

    Google Scholar 

  11. Misner, C. W.: In: Lectures in applied mathematics, Vol. 8, J. Ehlers, ed. Providence: American Mathematical Society 1967.

    Google Scholar 

  12. —— Taub, A. H.: Soviet. Phys. JEPT28, 122 (1969).

    Google Scholar 

  13. Sternberg, S.: Lectures on differential geometry. Englewood Cliffs: Prentice-Hall 1962.

    Google Scholar 

  14. Lang, S.: Introduction to differentiable manifolds, New York: Wiley 1962.

    Google Scholar 

  15. Whittaker, E. T., Watson, G. N.: A course of modern analysis. 4th ed. Cambridge: Univ. Press 1952.

    Google Scholar 

  16. Geroch, R. P.: J. Math. Phys.9, 450 (1968).

    Google Scholar 

  17. Trautman, A.: The applications of fibre bundles in physics. Preprint, Toruń, December, 1968.

Download references

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Authors and Affiliations

  1. Institute of Theoretical Physics, University of Berne, Switzerland

    Petr Hajicek

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  1. Petr Hajicek
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Hajicek, P. Extensions of the Taub and NUT spaces and extensions of their tangent bundles. Commun.Math. Phys. 17, 109–126 (1970). https://doi.org/10.1007/BF01646595

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  • DOI: https://doi.org/10.1007/BF01646595

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