Curvature Collineations of Some Plane Symmetric Static Spacetimes

Bokhari, Ashfaque H.; Kashif, A. R.; Qadir, Asghar

doi:10.1142/9789812701862_0024

Cited by 6 publications

(11 citation statements)

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“…On the one hand the metric conservation laws are pivotal to study the symmetry groups admitted by them, there are other tensors of more physical interest whose symmetries are wroth investigating. These tensors are given by Ricci and Riemann tensors and are fundamentally different from the metric tensor for their being degenerate unlike the metric tensor (Bokhari, 1992). The symmetries of these tensors are generally known as Ricci (RC) and curvature (CC) collineations.…”

Section: Introductionmentioning

confidence: 99%

Noether Symmetries Versus Killing Vectors and Isometries of Spacetimes

Bokhari

Kara

Kashif³

et al. 2006

Int J Theor Phys

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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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Section: Introductionmentioning

confidence: 99%

Noether Symmetries Versus Killing Vectors and Isometries of Spacetimes

Bokhari

Kara

Kashif³

et al. 2006

Int J Theor Phys

Self Cite

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“…Looking through the complete classification of spherically symmetric static metrics by KVs, CCs and RCs [13,14,15] did not yield any interesting case. We, therefore, looked at the corresponding classification of cylindrically symmetric static spacetimes [16,17,18] and plane symmetric static spacetimes [19,20,21] for this purpose.…”

Section: Examples Of Unequal {Wcs} and {Ccs}mentioning

confidence: 92%

Weyl Collineations That Are Not Curvature Collineations

Hussain

Qadir

Saifullah

2005

Int. J. Mod. Phys. D

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Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel." Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality."

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“…In case of CKVs, the function ψ(x a ) is called the conformal factor, while in the remaining cases it is called the inheriting factor. To understand the physics of spacetimes in general relativity, Ricci and matter collineations are extensively studied in the literature [2][3][4][5][6][7]18]. The inheriting symmetries including CKVs and CRCs are also investigated for certain physically important spacetimes.…”

Section: Introductionmentioning

confidence: 99%

Non-static spherically symmetric spacetimes and their conformal Ricci collineations

et al. 2019

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For a perfect fluid matter, we present a study of conformal Ricci collineations (CRCs) of non-static spherically symmetric spacetimes. For non-degenerate Ricci tenor, a vector field generating CRCs is found subject to certain integrability conditions. These conditions are then solved in various cases by imposing certain restrictions on the Ricci tensor components. It is found that non-static spherically symmetric spacetimes admit 5, 6 or 15 CRCs. In the degenerate case, it is concluded that such spacetimes always admit infinite number of CRCs.

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Curvature Collineations of Some Plane Symmetric Static Spacetimes

Abstract: We have found an error in one of the results in our paper. Our claim in Eq. (3) is not true. According to the correct version, all the Weyl tensor components in de Sitter/anti-de Sitter spacetimes are zero identically and therefore give arbitrary WCs and not 10 as claimed in our paper.

Cited by 6 publications

References 0 publications

Noether Symmetries Versus Killing Vectors and Isometries of Spacetimes

Noether Symmetries Versus Killing Vectors and Isometries of Spacetimes

Weyl Collineations That Are Not Curvature Collineations

Non-static spherically symmetric spacetimes and their conformal Ricci collineations

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