A Complete Classification of Curvature Collineations of Cylindrically Symmetric Static Metrics

Ashfaque H. Bokhari; Abdul R. Kashif; Asghar Qadir

doi:10.1023/A:1024068901739

A Complete Classification of Curvature Collineations of Cylindrically Symmetric Static Metrics

Ashfaque H. Bokhari^*
, Abdul R. Kashif
, Asghar Qadir

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

Curvature collineations are symmetry directions for the Riemann tensor, as isometries are for the metric tensor and Ricci collineations are for the Ricci tensor. Complete listings of many metrics possessing some minimal symmetry have been given for a number of symmetry groups for the latter two symmetries. It is shown that a claimed complete listing of cylindrically symmetric static metrics by their curvature collineations was actually incomplete and is completed here. It turns out that in this complete list, unlike the previous claim, there are curvature collineations that are distinct from the set of isometries and of Ricci collineations. The physical interpretation of some of the metrics obtained is given.

Original language	English
Pages (from-to)	1059-1076
Number of pages	18
Journal	General Relativity and Gravitation
Volume	35
Issue number	6
DOIs	https://doi.org/10.1023/A:1024068901739
State	Published - Jun 2003

Bibliographical note

Funding Information:
We are extremely grateful to an unknown referee for highly useful comments. AHB would like to thank United States Educational Foundation for the Fulbright grant. ARK would like to acknowledge financial support of the Mumtaz Riazuddin scholarship and AHB. AQ would like to thank KFUPM for their excellent research facilities.

Keywords

Curvature collineation
Cylindrically symmetric spacetime

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

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10.1023/A:1024068901739

Cite this

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title = "A Complete Classification of Curvature Collineations of Cylindrically Symmetric Static Metrics",

abstract = "Curvature collineations are symmetry directions for the Riemann tensor, as isometries are for the metric tensor and Ricci collineations are for the Ricci tensor. Complete listings of many metrics possessing some minimal symmetry have been given for a number of symmetry groups for the latter two symmetries. It is shown that a claimed complete listing of cylindrically symmetric static metrics by their curvature collineations was actually incomplete and is completed here. It turns out that in this complete list, unlike the previous claim, there are curvature collineations that are distinct from the set of isometries and of Ricci collineations. The physical interpretation of some of the metrics obtained is given.",

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note = "Funding Information: We are extremely grateful to an unknown referee for highly useful comments. AHB would like to thank United States Educational Foundation for the Fulbright grant. ARK would like to acknowledge financial support of the Mumtaz Riazuddin scholarship and AHB. AQ would like to thank KFUPM for their excellent research facilities.",

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PY - 2003/6

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N2 - Curvature collineations are symmetry directions for the Riemann tensor, as isometries are for the metric tensor and Ricci collineations are for the Ricci tensor. Complete listings of many metrics possessing some minimal symmetry have been given for a number of symmetry groups for the latter two symmetries. It is shown that a claimed complete listing of cylindrically symmetric static metrics by their curvature collineations was actually incomplete and is completed here. It turns out that in this complete list, unlike the previous claim, there are curvature collineations that are distinct from the set of isometries and of Ricci collineations. The physical interpretation of some of the metrics obtained is given.

AB - Curvature collineations are symmetry directions for the Riemann tensor, as isometries are for the metric tensor and Ricci collineations are for the Ricci tensor. Complete listings of many metrics possessing some minimal symmetry have been given for a number of symmetry groups for the latter two symmetries. It is shown that a claimed complete listing of cylindrically symmetric static metrics by their curvature collineations was actually incomplete and is completed here. It turns out that in this complete list, unlike the previous claim, there are curvature collineations that are distinct from the set of isometries and of Ricci collineations. The physical interpretation of some of the metrics obtained is given.

KW - Curvature collineation

KW - Cylindrically symmetric spacetime

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A Complete Classification of Curvature Collineations of Cylindrically Symmetric Static Metrics

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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