Topology of the Misner space and its \(g\)-boundary

  • Juan Margalef-Bentabol
  • Eduardo J. S. Villaseñor
Research Article

Abstract

The Misner space is a simplified 2-dimensional model of the 4-dimensional Taub-NUT space that reproduces some of its pathological behaviours. In this paper we provide an explicit base of the topology of the complete Misner space \(\mathbb {R}^{1,1}/boost\). Besides we prove that some parts of this space, that behave like topological boundaries, are equivalent to the \(g\)-boundaries of the Misner space.

Keywords

Misner space g-Boundary Spacetime topology 

References

  1. 1.
    Durin Bruno, B., Pioline, B.: Closed strings in misner space: a toy model for a big bounce?, String theory: from gauge interactions to cosmology. arXiv:hep-th/0501145v2, Springer, pp. 177–200 (2006)
  2. 2.
    Flores, J.L., Herrera, J., Sánchez, M.: Hausdorff separability of the boundaries for spacetimes and sequential spaces, Preprint (2014)Google Scholar
  3. 3.
    Geroch, R.: Local characterization of singularities in general relativity. J. Math. Phys. 9, 450 (1968)ADSCrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Geroch, R.: What is a singularity in general relativity? Ann. Phys. 48(3), 526–540 (1968)ADSCrossRefMATHGoogle Scholar
  5. 5.
    Geroch, R., Can-bin, L., Wald, R.M.: Singular boundaries of space–times. J. Math. Phys. 23, 432 (1982)ADSCrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Hajicek, P.: Embedding of singularities. Gen. Relativ. Gravit. 1(1), 27–29 (1970)ADSCrossRefGoogle Scholar
  7. 7.
    Hawking, S.W.: Singularities and the Geometry of Space–Time. Unpublished Essay Submitted for the Adams Prize. Cambridge University, Cambridge (1966)Google Scholar
  8. 8.
    Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space–Time. Cambrigde University Press, Cambrigde (1973)CrossRefMATHGoogle Scholar
  9. 9.
    Hikida, Y., Nayak, R.R., Panigrahi, K.L.: D-branes in a big bang/big crunch universe: Misner space. J. High Energy Phys. arXiv:hep-th/0508003v2 2005(09),023 (2005)
  10. 10.
    Javaloyes Victoria, M.A., Sánchez Caja, M.: An Introduction to Lorentzian Geometry and its Applications, Ed. Universidad de Sao Paulo, (2010)Google Scholar
  11. 11.
    Jonsson, R.M.: Visualizing curved spacetime. Am. J. Phys. arXiv:0708.2483v1
  12. 12.
    Lévy-Leblond, J.M.: Speed(s). Am. J. Phys. 48, 345–347 (1980)ADSCrossRefGoogle Scholar
  13. 13.
    Margalef Roig, J., Outerelo Domínguez, E.: Introducción a la topología, Ed. Complutense, (1993)Google Scholar
  14. 14.
    Misner, C.W.: Taub-NUT as a counterexample to almost anything. Tech. Rep. Uni. Maryland 529, 1–22 (1965)Google Scholar
  15. 15.
    Munkres, J.R.: Topology, vol. 2. Prentice Hall, Upper Saddle River (2000)Google Scholar
  16. 16.
    O’Neill, B.: Semi-Riemannian Geometry: With Applications to Relativity. Academic Press, New York (1983)MATHGoogle Scholar
  17. 17.
    Thorne, K.S.: Misner space as a prototype for almost any pathology, directions in general relativity: Papers in Honor of Charles Misner, 1, vol. 1, p. 333 (1993)Google Scholar
  18. 18.
    Willard, S.: General Topology. Courier Dover Publications, New York (2004)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Juan Margalef-Bentabol
    • 1
    • 2
  • Eduardo J. S. Villaseñor
    • 3
  1. 1.Instituto de Estructura de la MateriaCSICMadridSpain
  2. 2.Unidad Asociada al IEM-CSIC, Grupo de Teorías de Campos y Física Estadística, Instituto Universitario Gregorio Millán BarbanyGrupo de Modelización y Simulación Numérica, Universidad Carlos III de MadridMadridSpain
  3. 3.Unidad Asociada al IEM-CSIC, Grupo de Teorías de Campos y Física Estadística, Instituto Universitario Gregorio Millán Barbany, Grupo de Modelización y Simulación NuméricaUniversidad Carlos III de MadridMadridSpain

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