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General Relativity and Gravitation

, Volume 22, Issue 11, pp 1217–1227 | Cite as

Dynamical dimensional reduction

  • Marek Demiański
  • Marek Szydłowski
  • Jerzy Szczesny
Research Articles

Abstract

We propose to call a dynamical dimensional reduction effective if the corresponding dynamical system possesses a single attracting critical point representing expanding physical space-time and static internal space. We show that theBV × TD multidimensional cosmological model with a hydrodynamic energy-momentum tensor provides an example of effective dimensional reduction. We also study the dynamics of the multidimensional cosmological model of typeBI × TD with an energy-momentum tensor representing low temperature quantum effects, monopole contribution and the cosmological constant. It turns out that anisotropy and the cosmological constant are crucial for the process of dimensional reduction to be effective. We argue that this is the general property of homogeneous multidimensional cosmological models.

Keywords

Anisotropy Dynamical System Cosmological Constant General Property Dimensional Reduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Chodos, A., and Detweiler, S. (1980).Phys. Rev. D,21, 2167.Google Scholar
  2. 2.
    Demiański, M., Heller, M., Golda, Z., and Szydłowski, M. (1986).Class. Quant. Grav.,3, 1199; (1988).Class. Quant. Grav.,5, 733; Demiański, M., Heller, M., Szydłowski, M. (1987).Phys. Rev. D,36, 2945.Google Scholar
  3. 3.
    Maeda, K., and Nishino, H. (1985).Phys. Lett. B154, 358;B158, 381; Maeda, K. (1986).Class. Quant. Grav.,3, 233; Maeda, K., and Pang, P. Y. (1986).Phys. Lett. B180, 29.Google Scholar
  4. 4.
    Hartman, P. (1964).Ordinary Differential Equations, (Wiley, New York).Google Scholar
  5. 5.
    Demiański, M. Golda, Z., Sokołowski, L., Szydłowski, M., Turkowski, P. (1987).J. Math. Phys.,28, 171.Google Scholar
  6. 6.
    Candelas, P., and Weinberg, S. (1982).Nucl. Phys. B209, 149; Yoshimura, M. (1984).Phys. Rev. D,30, 344.Google Scholar
  7. 7.
    Gleiser, M., Rajpoot, S., and Taylor, J. G. (1985).Ann. Phys.,160, 299; Lorentz-Petzold, D. (1984).Phys. Lett.,B148, 43; (1984).B153, 134; (1985).Phys. Rev. D,31, 929.Google Scholar
  8. 8.
    Okada, Y. (1985).Phys. Lett.,B150, 103; Wiltshire, D. L. (1987).Phys. Rev. D,36, 1634.Google Scholar
  9. 9.
    Accetta, F. S., Gleiser, M., Holman, R., and Kolb, E. W. (1986).Nucl. Phys. B276, 501.Google Scholar
  10. 10.
    Szydłowski, M., Szczesny, J., and Biesiada, M. (1987).Class. Quant. Grav.,4, 1731; Szydłowski, M., and Szczesny, J. (1988).Phys. Rev. D,38, 9625; Szydłowski, M., Szczesny, J., and Stawicki, T. (1988).Class. Quant. Grav.,5, 1097. Biesiada, M., and Szydłowski, M. (1990).Phys. Lett.,A145, 401.Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Marek Demiański
    • 1
  • Marek Szydłowski
    • 2
  • Jerzy Szczesny
    • 3
  1. 1.Institute for Theoretical PhysicsWarsaw UniversityWarsawPoland
  2. 2.Astronomical ObservatoryJagellonian UniversityKrakówPoland
  3. 3.Institute of PhysicsJagellonian UniversityKrakówPoland

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