Noether symmetries versus killing vectors and isometries of spacetimes

A. H. Bokhari; A. H. Kara; A. R. Kashif; F. D. Zaman

doi:10.1007/s10773-006-9096-1

Noether symmetries versus killing vectors and isometries of spacetimes

A. H. Bokhari^*, A. H. Kara, A. R. Kashif, F. D. Zaman

^*Corresponding author for this work

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

41 Scopus citations

Abstract

Symmetries of spacetime manifolds which are given by Killing vectors are compared with the symmetries of the Lagrangians of the respective spacetimes. We find the point generators of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian (Noether symmetries). In the examples considered, it is shown that the Noether symmetries obtained by considering the Larangians provide additional symmetries which are not provided by the Killing vectors. It is conjectured that these symmetries would always provide a larger Lie algebra of which the KV symmetres will form a subalgebra.

Original language	English
Pages (from-to)	1063-1073
Number of pages	11
Journal	International Journal of Theoretical Physics
Volume	45
Issue number	6
DOIs	https://doi.org/10.1007/s10773-006-9096-1
State	Published - Jun 2006

Bibliographical note

Funding Information:
AHK thanks the N.R.F. of South Africa for financial support. We are also thankful to KFUPM for providing facilities to complete this work.

Keywords

Isometries of spacetimes
Lie algebras
Noether symmetries

ASJC Scopus subject areas

General Mathematics
Physics and Astronomy (miscellaneous)

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10.1007/s10773-006-9096-1

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abstract = "Symmetries of spacetime manifolds which are given by Killing vectors are compared with the symmetries of the Lagrangians of the respective spacetimes. We find the point generators of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian (Noether symmetries). In the examples considered, it is shown that the Noether symmetries obtained by considering the Larangians provide additional symmetries which are not provided by the Killing vectors. It is conjectured that these symmetries would always provide a larger Lie algebra of which the KV symmetres will form a subalgebra.",

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note = "Funding Information: AHK thanks the N.R.F. of South Africa for financial support. We are also thankful to KFUPM for providing facilities to complete this work.",

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AU - Bokhari, A. H.

AU - Kara, A. H.

AU - Kashif, A. R.

AU - Zaman, F. D.

N1 - Funding Information: AHK thanks the N.R.F. of South Africa for financial support. We are also thankful to KFUPM for providing facilities to complete this work.

PY - 2006/6

Y1 - 2006/6

N2 - Symmetries of spacetime manifolds which are given by Killing vectors are compared with the symmetries of the Lagrangians of the respective spacetimes. We find the point generators of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian (Noether symmetries). In the examples considered, it is shown that the Noether symmetries obtained by considering the Larangians provide additional symmetries which are not provided by the Killing vectors. It is conjectured that these symmetries would always provide a larger Lie algebra of which the KV symmetres will form a subalgebra.

AB - Symmetries of spacetime manifolds which are given by Killing vectors are compared with the symmetries of the Lagrangians of the respective spacetimes. We find the point generators of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian (Noether symmetries). In the examples considered, it is shown that the Noether symmetries obtained by considering the Larangians provide additional symmetries which are not provided by the Killing vectors. It is conjectured that these symmetries would always provide a larger Lie algebra of which the KV symmetres will form a subalgebra.

KW - Isometries of spacetimes

KW - Lie algebras

KW - Noether symmetries

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M3 - Article

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JO - International Journal of Theoretical Physics

JF - International Journal of Theoretical Physics

IS - 6

ER -

Noether symmetries versus killing vectors and isometries of spacetimes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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