Ricci Flows and Topology Change in Quantum Gravity
American Journal of Modern Physics
Volume 2, Issue 3, May 2013, Pages: 132-137
Received: Feb. 10, 2013; Published: May 2, 2013
Views 2780      Downloads 145
Author
Vladimir Dzhunushaliev, 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
Article Tools
PDF
Follow on us
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.
Keywords
Ricci Flow, Topology Change, Statistical System, Wormhole
To cite this article
Vladimir Dzhunushaliev, Ricci Flows and Topology Change in Quantum Gravity, American Journal of Modern Physics. Vol. 2, No. 3, 2013, pp. 132-137. doi: 10.11648/j.ajmp.20130203.16
References
[1]
J. Wheeler, Ann. of Phys., 2, 604(1957); J.A. Wheeler: Geometrodynamics, Academic Press, USA (1962).
[2]
Y. Choquet-Bruhat and R. Geroch, Commun. Math. Phys. 14, 329-350 (1969).
[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].
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186