Soviet Physics Journal

, Volume 28, Issue 1, pp 82–86 | Cite as

Scalar-tensor approach to the derivation of a theory of topological transitions

  • M. Yu. Konstantinov
Physics of Elementary Particles and Field Theory
  • 9 Downloads

Abstract

The derivation of a classical theory of gravitation whose solutions explicitly contain a description of topological transitions is discussed. Toward this goal there is a discussion of a scalar-tensor formalism based on the representation of a certain subclass of spacelike hypersurfaces as surfaces of a constant level of a smooth function on a four-dimensional manifold. The solutions of a theory of this type, along with the Lorentzian structure of space-time and the topology of space-like hypersurfaces, determine a frame of reference, but the nature of the topological transitions does not depend on the choice of a frame of reference. This independence proves the correctness of this new approach. Two versions of a scalar-tensor theory of topological transitions are considered as examples. One version reduces to Einstein's theory of gravitation in a regular region of space-time, while the other is a nontrivial modification of the Brans-Dicke theory.

Keywords

Manifold Smooth Function Classical Theory Constant Level Spacelike Hypersurface 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    M. Yu. Konstantinov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 55 (1983).Google Scholar
  2. 2.
    J. A. Wheeler, Einstein's Foresights [Russian translation], Mir, Moscow (1970).Google Scholar
  3. 3.
    R. Brill and R. H. Gowdy, in: Quantum Gravitation and Topology [Russian translation], Mir, Moscow (1973), pp. 66–179.Google Scholar
  4. 4.
    S. W. Hawking, Nucl. Phys.,B114, 349 (1978).Google Scholar
  5. 5.
    D. Ivanenko, in: Relativistic Quanta and Cosmology, Reprint Corp., New York (1980), p. 295.Google Scholar
  6. 6.
    V. N. Ponomarev, in: Proceedings of the All-Union Conference on Modern Theoretical and Experimental Problems of the Theory of Relativity and Gravitation, July 1981, Moscow [in Russian], MGU, Moscow (1981), p. 240.Google Scholar
  7. 7.
    B. De Witt, in: Tenth International Conference on General Relativity and Gravitation, Padova, July 4–9, 1983, Contrib. Pap. Vol. 2, Rome (1983), p. 1016.Google Scholar
  8. 8.
    M. Yu. Konstantinov, in: Tenth International Conference on General Relativity and Gravitation, Padova, July 4–9, 1983, Contrib. Pap. Vol. 2, Roma (1983), pp. 1110–1112.Google Scholar
  9. 9.
    M. Yu. Konstantinov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 12, 42 (1983).Google Scholar
  10. 10.
    M. Yu. Konstantinov and V. N. Mel'nikov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 8, 32 (1984).Google Scholar
  11. 11.
    A. T. Fomenko, Differential Geometry and Topology: Supplementary Chapters [in Russian], MGU, Moscow (1983).Google Scholar
  12. 12.
    Yu. S. Vladimirov, Frames of Reference in the General Theory of Relativity [in Russian], Energoatomizdat, Moscow (1982).Google Scholar
  13. 13.
    C. Brans and R. Dicke, Phys. Rev.,124, 965 (1961).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • M. Yu. Konstantinov

There are no affiliations available

Personalised recommendations