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Ricci Flows and Topology Change in Quantum Gravity

Received: 10 February 2013    Accepted:     Published: 2 May 2013
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Abstract

The topology change in quantum gravity is modeled by a Ricci flow. In this approach we consider the Ricci flow as a statistical system. The metric in the Ricci flow enumerated by a parameter is a microscopical statistical state. The probability of every microscopical state is determined by this parameter. The Ricci flow starting from a static wormhole filled with a phantom Sine-Gordon scalar field is investigated numerically.

Published in American Journal of Modern Physics (Volume 2, Issue 3)
DOI 10.11648/j.ajmp.20130203.16
Page(s) 132-137
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Ricci Flow, Topology Change, Statistical System, Wormhole

References
[1] J. Wheeler, Ann. of Phys., 2, 604(1957); J.A. Wheeler: Geometrodynamics, Academic Press, USA (1962).
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[3] A. Borde, Bull. Astr. Soc. India 25, 571-577 (1997).
[4] G.T. Horowitz, Class. Quant. Grav. 8, 587-601 (1991).
[5] H.F. Dowker and R.S. Garcia, Class. Quant. Grav. 15, 1859-1879 (1998); H.F. Dowker, Topology change in quan-tum gravity, in ``The future of theoretical physics and cosmology'', eds. G.W. Gibbons, S.J. Rankin, E.P.S. Shellard, Cambridge Univ. Press, p.879, (2003).
[6] R.D. Sorkin and S. Surya, Int. J. Mod. Phys. A 13, 3749-3790 (1998).
[7] P. Csizmadia and I. Racz, Class. Quant. Grav. 27, 015001 (2010) [arXiv:0911.2373 [gr-qc]].
[8] R. Hamilton, J. Diff. Geom., 17, 255 (1982).
[9] G. Perelman, preprint [arxiv:math.DG/0211159]; preprint [arxiv:math.DG/0303109].
[10] Morris W. Hirsch, ''Differential topology``, (Springer-Verlag, New-York-Heidelberg-Berlin, 1976).
[11] V. Dzhunushaliev, Int. J. Geom. Meth. Mod. Phys., 6, 1033-1046 (2009); arXiv:0809.0957 [gr-qc].
[12] P. Topping, Lectures on the Ricci Flow, London Mathe-matical Society Lecture Notes Series 325, Cambridge University Press (2006).
[13] V. Dzhunushaliev and V. Folomeev, `Creation/annihilation of wormholes supported by the Sine-Gordon phantom (ghost) field,'' arXiv:0909.2739 [gr-qc].
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    Vladimir Dzhunushaliev. (2013). Ricci Flows and Topology Change in Quantum Gravity. American Journal of Modern Physics, 2(3), 132-137. https://doi.org/10.11648/j.ajmp.20130203.16

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    ACS Style

    Vladimir Dzhunushaliev. Ricci Flows and Topology Change in Quantum Gravity. Am. J. Mod. Phys. 2013, 2(3), 132-137. doi: 10.11648/j.ajmp.20130203.16

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    AMA Style

    Vladimir Dzhunushaliev. Ricci Flows and Topology Change in Quantum Gravity. Am J Mod Phys. 2013;2(3):132-137. doi: 10.11648/j.ajmp.20130203.16

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  • @article{10.11648/j.ajmp.20130203.16,
      author = {Vladimir Dzhunushaliev},
      title = {Ricci Flows and Topology Change in Quantum Gravity},
      journal = {American Journal of Modern Physics},
      volume = {2},
      number = {3},
      pages = {132-137},
      doi = {10.11648/j.ajmp.20130203.16},
      url = {https://doi.org/10.11648/j.ajmp.20130203.16},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20130203.16},
      abstract = {The topology change in quantum gravity is modeled by a Ricci flow. In this approach we consider the Ricci flow as a statistical system. The metric in the Ricci flow enumerated by a parameter   is a microscopical statistical state. The probability of every microscopical state is determined by this parameter. The Ricci flow starting from a static wormhole filled with a phantom Sine-Gordon scalar field is investigated numerically.},
     year = {2013}
    }
    

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    AU  - Vladimir Dzhunushaliev
    Y1  - 2013/05/02
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    N1  - https://doi.org/10.11648/j.ajmp.20130203.16
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    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
    SP  - 132
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    AB  - The topology change in quantum gravity is modeled by a Ricci flow. In this approach we consider the Ricci flow as a statistical system. The metric in the Ricci flow enumerated by a parameter   is a microscopical statistical state. The probability of every microscopical state is determined by this parameter. The Ricci flow starting from a static wormhole filled with a phantom Sine-Gordon scalar field is investigated numerically.
    VL  - 2
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    ER  - 

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Author Information
  • Dept. Theor. and Nucl. Phys., Kazakh National University, Almaty, 010008, Kazakhstan; Institute of Physicotechnical Problems and Material Science of the NAS of the Kyrgyz Republic, 265 a, Chui Street, Bishkek, 720071,Kyrgyz Republic

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