Noether versus Killing symmetry of conformally flat Friedmann metric

Bokhari, Ashfaque H.; Kara, A. H.

doi:10.1007/s10714-007-0501-8

Cited by 43 publications

(27 citation statements)

References 17 publications

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“…Recent work in this direction has been by Bokhari et all ( [11], [12]) in which the relation of the Noether symmetries with the KVs of some special spacetimes it is discussed.…”

Section: Collineations (Ac) Homothetic Killing Vector (Hkv) and Killmentioning

confidence: 99%

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Lie and Noether symmetries of geodesic equations and collineations

2010

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The Lie symmetries of the geodesic equations in a Riemannian space are computed in terms of the special projective group and its degenerates (affine vectors, homothetic vector and Killing vectors) of the metric.The Noether symmetries of the same equations are given in terms of the homothetic and the Killing vectors of the metric. It is shown that the geodesic equations in a Riemannian space admit three linear first integrals and two quadratic first integrals. We apply the results in the case of Einstein spaces, the Schwarzschild spacetime and the Friedman Robertson Walker spacetime. In each case the Lie and the Noether symmetries are computed explicitly together with the corresponding linear and quadratic first integrals.

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“…Recent work in this direction has been by Bokhari et all ( [11], [12]) in which the relation of the Noether symmetries with the KVs of some special spacetimes it is discussed.…”

Section: Collineations (Ac) Homothetic Killing Vector (Hkv) and Killmentioning

confidence: 99%

“…In a recent paper Bokhari and Kara [12] In the following we compute all the Noether symmetries of the FRW spacetimes. To do that we have to have the homothetic algebra of these models [19].…”

Section: The Noether Symmetries Of the Frw Metricsmentioning

confidence: 99%

Lie and Noether symmetries of geodesic equations and collineations

2010

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“…Thus they gave a conjecture that the Noether symmetries form a bigger set of Lie algebra and the Killing symmetries are a subset of that algebra. A similar comparison of Killing and Noether symmetries was given for conformally flat Friedmann metric [22]. Hall [23] gave a general relation connecting the dimensions of the Killing algebra, the orbits and the isotropies of the spacetime.…”

Section: Introductionmentioning

confidence: 75%

“…An isometry is a direction along which Lie derivative of the metric tensor is zero. It would be worthwhile to mention here that many GR solutions do have some symmetry [7]. The problem of localization of energy momentum in GR can be addressed using symmetries.…”

Section: Introductionmentioning

confidence: 99%

Killing and Noether Symmetries of Plane Symmetric Spacetime

2013

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This paper is devoted to investigate the Killing and Noether symmetries of static plane symmetric spacetime. For this purpose, five different cases have been discussed. The Killing and Noether symmetries of Minkwoski spacetime in cartesian coordinates are calculated as a special case and it is found that Lie algebra of the Lagrangian is 10 and 17 dimensional respectively. The symmetries of Taub's universe, anti-deSitter universe, self similar solutions of infinite kind for parallel perfect fluid case and self similar solutions of infinite kind for parallel dust case are also explored. In all the cases, the Noether generators are calculated in the presence of gauge term. All these examples justify the conjecture that Killing symmetries form a subalgebra of Noether symmetries [1].

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“…Bokhari and Kara [12] studied Noether symmetries in conformally flat Friedmann metric and compared their results with KVs. According to their analysis, the flat Friedmann metric admits additional conservation laws not given by KVs.…”

Section: Introductionmentioning

confidence: 99%

Energy conditions and conservation laws in LTB metric via Noether symmetries

Hussain

Akhtar

2018

Eur. Phys. J. C

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In this paper, we have investigated Noether symmetries in Lemaitre-Tolman-Bondi (LTB) metric. Using the Lagrangian associated with the LTB metric, the set of determining equations for Noether symmetries is obtained and then integrated in several cases. It is shown that the LTB metric can be classified in to eight distinct classes corresponding to Noether algebra of dimension 4, 5, 6, 7, 8, 9, 11 and 17. The obtained Noether symmetries are compared with Killing and homothetic vectors. The well known Noether's theorem is used to find the expressions for conservation laws in each case. Moreover, it is shown that most of the obtained metrics are anisotropic or perfect fluid models which satisfy certain energy conditions and the equation of state.

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Noether versus Killing symmetry of conformally flat Friedmann metric

Cited by 43 publications

References 17 publications

Lie and Noether symmetries of geodesic equations and collineations

Lie and Noether symmetries of geodesic equations and collineations

Killing and Noether Symmetries of Plane Symmetric Spacetime

Energy conditions and conservation laws in LTB metric via Noether symmetries

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