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Einstein tensor and generalizations of Birkhoff's theorem

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Abstract

The Einstein tensors of metrics having a 3-parameter group of (global) isometries with 2-dimensional non-null orbitsG 3(2,s/t) are studied in order to obtainalgebraic conditions guaranteeing an additional normal Killing vector. It is shown that Einstein spaces withG 3(2,s/t) allow aG 4. A critical review of some of the literature on Birkhoff's theorem and its generalizations is given.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Göttingen, Germany

    Hubert Goenner

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  1. Hubert Goenner
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This work was started at the Department of Physics, Temple University, Philadelphia, Pa., and supported there by the Aerospace Research Laboratories of the Office of Aerospace Research, U.S.A.F.

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Goenner, H. Einstein tensor and generalizations of Birkhoff's theorem. Commun.Math. Phys. 16, 34–47 (1970). https://doi.org/10.1007/BF01645493

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