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Soviet Physics Journal

, Volume 19, Issue 9, pp 1136–1138 | Cite as

Vacuum Einstein spaces with axial symmetry

  • R. F. Bilyalov
Article
  • 13 Downloads

Abstract

Four classes of solutions are found to the equations Rαβ=−2σ σ and gαβ σ;αβ=0 in three-dimensional space with metric gαβdxαdxβ and signature (+ −−), equivalent to the Einstein equations Rij=0 in a vacuum for the metric\(ds^2 = e^{2\sigma } g_{\alpha \beta } dx^\alpha dx^\beta - e^{ - 2\sigma } \times dx^{3^2 }\). The metric ds2 assumes axial symmetry and symmetry with respect to the reflection\(x^{3^1 } = x^3\).

Keywords

Reflection Axial Symmetry Einstein Equation Einstein Space 
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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Literature cited

  1. 1.
    E. Newman and R. Penrose, J. Math. Phys.,3, 566 (1962).Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • R. F. Bilyalov
    • 1
  1. 1.V. I. Ul'yanov-Lenin Kazan State UniversityUSSR

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