Soviet Physics Journal

, Volume 22, Issue 5, pp 468–472 | Cite as

Time-dependent solutions with localized energy of the Einstein system of equations and a nonlinear scalar field

  • V. N. Mel'nikov
  • G. N. Shikin
Article
  • 20 Downloads

Abstract

A soliton-like time-dependent solution in the form of a running wave is derived of a self-consistent system of the gravitational field equations of Einstein and Born-Infeld type of equations of a nonlinear scalar field in a conformally flat metric. This solution is localized in space and possesses a localized energy. It is shown that both the gravitational field and the nonlinearity of the scalar field are essential to the presence of such a localized solution. In recent years various classical particle models have been widely discussed which are static or time-independent solutions of nonlinear equations with localization in space and which possess a finite field energy. In particular, soliton solutions [1], solutions in the form of eddies [2], and so on have been derived and investigated. All these solutions were treated in a flat space-time. It is of interest to derive the analogous particle-like solutions with the gravitational field taken into account; in particular it is of interest to investigate the roles of the gravitational field in connection with the formation of localized objects. These problems have been discussed in [3] in the static case. We will present below a soliton-like time-dependent solution in the form of a solitary running wave as an example of the inter-action of a Born-Infeld type of nonlinear scalar field and an Einstein gravitational field in a conformally flat metric.

Keywords

Soliton Scalar Field Gravitational Field Finite Field Soliton Solution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    V. E. Korepin and L. D. Faddeev, Teor. Mat. Fiz.,25, No. 2, 147 (1975).Google Scholar
  2. 2.
    H. B. Nielsen and P. Olesen, Nucl. Phys.,B61, 45 (1973).Google Scholar
  3. 3.
    K. A. Bronnikov, V. N. Mel'nikov, and G. N. Shikin, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 11 (1978).Google Scholar
  4. 4.
    D. D. Ivanenko, in: Nonlinear Quantum Field Theory [Russian translation], IL, Moscow (1959), p. 3.Google Scholar
  5. 5.
    G. N. Shikin, in: Problems of the Theory of Gravitation and Elementary Particles [in Russian], No. 7, Atomizdat, Moscow (1976).Google Scholar
  6. 6.
    D. I. Blokhintsev, Usp. Fiz. Nauk,61, 2, 137 (1957).Google Scholar
  7. 7.
    D. I. Blokhintsev, Dokl. Akad. Nauk SSSR,82, 553 (1952).Google Scholar
  8. 8.
    G. N. Shikin, in: Relativity Theory and Gravitation [in Russian], Nauka, Moscow (1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • V. N. Mel'nikov
    • 1
  • G. N. Shikin
    • 1
  1. 1.All-Union Scientific-Research Institute of Physicotechnical and Radio Engineering MeasurementsUSSR

Personalised recommendations