Classification of Cylindrically Symmetric Static Spacetimes according to Their Ricci Collineations

Asghar Qadir*, K. Saifullah, M. Ziad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


A complete classification of cylindrically symmetric static Lorentzian manifolds according to their Ricci collineations (RCs) is provided. The Lie algebras of RCs for the non-degenerate Ricci tensor have dimensions 3 to 10, excluding 8 and 9. For the degenerate tensor the algebra is mostly but not always infinite dimensional; there are cases of 10-, 5-, 4- and 3-dimensional algebras. The RCs are compared with the Killing vectors (KVs) and homothetic motions (HMs). The (non-linear) constraints corresponding to the Lie algebras are solved to construct examples which include some exact solutions admitting proper RCs. Their physical interpretation is given. The classification of plane symmetric static spacetimes emerges as a special case of this classification when the cylinder is unfolded.

Original languageEnglish
Pages (from-to)1927-1975
Number of pages49
JournalGeneral Relativity and Gravitation
Issue number11
Publication statusPublished - Nov 2003
Externally publishedYes


  • Cylindrical symmetry
  • Ricci collineation

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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