Energy Content of Colliding Plane Waves Using Approximate Noether Symmetries

Sharif, M.; Waheed, Saira

doi:10.1007/s13538-012-0071-4

Cited by 8 publications

(7 citation statements)

References 38 publications

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“…Using the ANGS for the Schwarzschild and Kerr metrics, Hussain et al [22] have recovered all the lost conservation laws as trivial first-order approximate conservation laws in first-order approximate case. Using approximate Lie symmetries the energy content of colliding plane waves have studied by Sharif and Waheed [23]. By analyzing the behavior of the effective potential for the particles and photons, it is investigated the time-like and null geodesic structures for the Bardeen metric [24].…”

Section: Introductionmentioning

confidence: 99%

Approximate Noether gauge symmetries of the Bardeen model

Camcı

2014

Eur. Phys. J. C

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Section: Introductionmentioning

confidence: 99%

Approximate Noether gauge symmetries of the Bardeen model

Camcı

2014

Eur. Phys. J. C

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“…In this respect, Hussain et al [32] used the concept of approximate symmetries of geodesic equations and investigated energy re-scaling for Reissner-Nordström spacetime. Sharif and Waheed [33][34][35] calculated the energy contents of some black holes as well as plane colliding gravitational waves using approximate symmetries. In f (R) gravity, several researchers [36][37][38][39][40][41][42][43] have discussed exact FRW solutions by exploring corresponding Noether symmetries as well as conserved quantities.…”

Section: Introductionmentioning

confidence: 99%

Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

2021

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The present article investigates the existence of Noether and Noether gauge symmetries of flat Friedman–Robertson–Walker universe model with perfect fluid matter ingredients in a generalized scalar field formulation namely $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by $$Y=R_{\alpha \beta }R^{\alpha \beta }$$ Y = R α β R α β , while $$\phi $$ ϕ represents scalar field. For this purpose, we assume different general cases of generic $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) function and explore its possible forms along with field potential $$V(\phi )$$ V ( ϕ ) by taking constant and variable coupling function of scalar field $$\omega (\phi )$$ ω ( ϕ ) . In each case, we find non-trivial symmetry generator and its related first integrals of motion (conserved quantities). It is seen that due to complexity of the resulting system of Lagrange dynamical equations, it is difficult to find exact cosmological solutions except for few simple cases. It is found that in each case, the existence of Noether symmetries leads to power law form of scalar field potential and different new types of generic function. For the acquired exact solutions, we discuss the cosmology generated by these solutions graphically and discuss their physical significance which favors the accelerated expanding eras of cosmic evolution.

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“…Recently, Ali and Feroze [23] have provided a classification of plane symmetric static spacetimes considering Noether gauge symmetry approach. Using the approximate Noether symmetries the energy contents of some classes of colliding plane waves are calculated by Sharif and Waheed [24]. Camci [25] has obtained the NGSs of geodesic Lagrangian L and explicitly integrated the geodesic equations of motion for the corresponding stationary Gödel-type spacetimes.…”

Section: Introductionmentioning

confidence: 99%

Noether gauge symmetry classes for pp-wave spacetimes

Camcı

Yildirim

2015

Int. J. Geom. Methods Mod. Phys.

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The Noether gauge symmetries of geodesic Lagrangian for the pp-wave spacetimes are determined in each of the Noether gauge symmetry classes of the pp-wave spacetimes. It is shown that a type N pp-wave spacetime can admit at most three Noether gauge symmetry, and furthermore the number of Noether gauge symmetries turn out to be four, five, six, seven and eight. We found that all conformally flat plane wave spacetimes admit the maximal, i.e. ten, Noether gauge symmetry. Also it is found that if the pp-wave spacetime is nonconformally flat plane wave, then the number of Noether gauge symmetry is nine or ten. By means of the obtained Noether constants the search of the exact solutions of the geodesic equations for the pp-wave spacetimes is considered and we found new exact solutions of the geodesic equations in some special Noether gauge symmetry classes.

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Energy Content of Colliding Plane Waves Using Approximate Noether Symmetries

Cited by 8 publications

References 38 publications

Approximate Noether gauge symmetries of the Bardeen model

Approximate Noether gauge symmetries of the Bardeen model

Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

Noether gauge symmetry classes for pp-wave spacetimes

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