Classification of plane-symmetric Lorentzian manifolds according to their homotheties and metrics

M Ziad Bashir*, Sadia Ehsan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Plane-symmetric Lorentzian manifolds are classified according to their homothetic vector fields and metrics or classes of metrics. It is found that these manifolds can admit 4, 5, 7 and 11 dimensional homothetic Lie algebras. Explicit self-similar metrics are obtained corresponding to the homothetic Lie algebras of dimensions greater than or equal to five. For four-dimensional homothetic Lie algebras, there appear classes of self-similar metrics, with metric coefficients related by non-linear differential constraints. Explicit examples are provided to ensure the existence of proper homothetic vector fields in the cases where the metrics are given implicitly. Later, using this classification, self-similar metrics are found which represent perfect-fluid solutions of the Einstein field equations.

Original languageUndefined/Unknown
Pages (from-to)71-83
Number of pages13
JournalNuovo Cimento della Societa Italiana di Fisica. B, General Physics, Relativity, Astronomy and Mathematical Physics and Methods
Issue number1
Publication statusPublished - 2008

ASJC Scopus subject areas

  • General Physics and Astronomy

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