General Relativity and Gravitation

, Volume 28, Issue 5, pp 537–548 | Cite as

Some D type metric forms for spacetimes with shear, nongeodesic, and nondiverging principal null congruences

  • Jerzy Klemens Kowalczyński


In the context of a null tetrad formalism it is assumed that the two real vectors of the tetrad have neither expansion nor rotation and that they are nongeodesic and/or have shear. This assumption is rarely used in search of algebraically special spacetimes. General relations for the connection and for the Ricci and Weyl tensors are presented. An additional assumption that these vectors are principal leads to Petrov type D spacetimes, reducible in some cases to conformally flat ones. Twenty-two explicit metric forms, probably hitherto unknown, are found.


General Relation Differential Geometry Additional Assumption Real Vector Weyl Tensor 
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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Jerzy Klemens Kowalczyński
    • 1
  1. 1.Institute of PhysicsPolish Academy of SciencesWarsawPoland

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