Soviet Physics Journal

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

Vacuum Einstein spaces with axial symmetry

  • R. F. Bilyalov


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\(x^{3^1 } = x^3\).


Reflection Axial Symmetry Einstein Equation Einstein Space 
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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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