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Three-dimensional space-times

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Abstract

A real version of the Newman-Penrose formalism is developed for (2+1)-dimensional space-times. The complete algebraic classification of the (Ricci) curvature is given. The field equations of Deser, Jackiw, and Templeton, expressing balance between the Einstein and Bach tensors, are reformulated in triad terms. Two exact solutions are obtained, one characterized by a null geodesic eigencongruence of the Ricci tensor, and a second for which all the polynomial curvature invariants are constant.

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Authors and Affiliations

  1. Department of Mathematics, University of Aberdeen, AB9 2TY, Aberdeen, Great Britain

    G. S. Hall

  2. Department of Physics, University of Nebraska, 68588-0111, Lincoln, Nebraska, USA

    T. Morgan

  3. Central Research Institute for Physics, P.O.B. 49, H-1525, Budapest 114, Hungary

    Z. Perjés

Authors
  1. G. S. Hall
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  2. T. Morgan
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  3. Z. Perjés
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Hall, G.S., Morgan, T. & Perjés, Z. Three-dimensional space-times. Gen Relat Gravit 19, 1137–1147 (1987). https://doi.org/10.1007/BF00759150

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  • DOI: https://doi.org/10.1007/BF00759150

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