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


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.


Soliton Scalar Field Gravitational Field Finite Field Soliton Solution 
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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

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