Communications in Mathematical Physics

, Volume 16, Issue 1, pp 34–47 | Cite as

Einstein tensor and generalizations of Birkhoff's theorem

  • Hubert Goenner


The Einstein tensors of metrics having a 3-parameter group of (global) isometries with 2-dimensional non-null orbitsG3(2,s/t) are studied in order to obtainalgebraic conditions guaranteeing an additional normal Killing vector. It is shown that Einstein spaces withG3(2,s/t) allow aG4. A critical review of some of the literature on Birkhoff's theorem and its generalizations is given.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Critical Review 
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Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • Hubert Goenner
    • 1
  1. 1.Institut für Theoretische PhysikUniversität GöttingenGermany

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