New spherically symmetric solutions in f (R)-gravity by Noether symmetries

We explore the recently introduced modified Gauss-Bonnet gravity (Sharif and Ikram in Eur Phys J C 76:640, 2016), f (G, T ) pragmatic with G, the Gauss-Bonnet term, and T , the trace of the energy-momentum tensor. Noether symmetry approach has been used to develop some cosmologically viable f (G, T ) gravity models. The Noether equations of modified gravity are reported for flat FRW universe. Two specific models have been studied to determine the conserved quantities and exact solutions. In particular, the well known deSitter solution is reconstructed for some specific choice of f (G, T ) gravity model.

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“…Since the Lagrangian L is invariant along the vector field W, consequently the definition for Noether current turns out to be [53] …”

Section: Noether Symmetries and F (G T ) Gravitymentioning

confidence: 99%

Noether symmetry approach in $$f(\mathcal {G},T)$$ f ( G , T ) gravity

2017

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“…The presence of Noether symmetries allows one to reduce the dynamics and find out exact solutions as well as the analytic form of f (R) [9,11].…”

Section: Noether Symmetrymentioning

confidence: 99%

“…This approach has also been used to obtain f (T ) gravity models respecting the Noether symmetry [10]. On the other hand, new spherically symmetric solutions in f (R) gravity have been obtained by Noether Symmetries [11]. In the present paper, we apply the Noether symmetry approach to obtain (2 + 1) dimensional black hole solutions in f (R) gravity which are consistent with the Noether symmetry.…”

Section: Introductionmentioning

confidence: 95%

Generalized (2+1) dimensional black hole by Noether symmetry

2013

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We use the Noether symmetry approach to find f (R) theory of (2 + 1) dimensional gravity and (2 + 1) dimensional black hole solution consistent with this f (R) gravity and the associated symmetry. We obtainwhere the constant term D 3 plays no dynamical role. Then, we find general spherically symmetric solution for this f (R) gravity which is potentially capable of being as a black hole. Moreover, in the special case, we obtain a generalized BTZ black hole which, other than common conserved charges m and J, contains a new conserved charge Q. It is shown that this conserved charge corresponds to the freedom in the choice of the constant term D 3 and represents symmetry of the action under the transformation R → R ′ = R + D 3 along the killing vector ∂ R . The ordinary BTZ black hole is obtained as the special case where D 3 is fixed to be proportional to the infinitesimal cosmological constant and consequently the symmetry is broken via Q = 0. We study the thermodynamics of the generalized BTZ black hole and show that its entropy can be described by the Cardy-Verlinde formula.

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“…Since the Lagrangian L remains unchanged along the vector field W, as a result, the definition of Noether current turns out to be [46] …”

Section: Noether Symmetries and F (G T ) Gravitymentioning

confidence: 99%

Some exact solutions in f(𝒢,T) gravity via Noether symmetries

Shamir

Ahmad

2017

Mod. Phys. Lett. A

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This paper is devoted to investigate the recently proposed modified Gauss-Bonnet f (G, T ) gravity, with G, the Gauss-Bonnet term, coupled with T , the trace of energy-momentum tensor. We have used the Noether symmetry methodology to discuss some cosmologically important f (G, T ) gravity models with anisotropic background. In particular, the Noether symmetry equations for modified f (G, T ) gravity are reported for locally rotationally symmetric Bianchi type I universe. Explicitly, two models have been proposed to explore the exact solutions and the conserved quantities. It is concluded that the specific models of modified Gauss-Bonnet gravity may be used to reconstruct ΛCDM cosmology without involving any cosmological constant.

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New spherically symmetric solutions in f (R)-gravity by Noether symmetries

Cited by 85 publications

References 38 publications

Noether symmetry approach in $$f(\mathcal {G},T)$$ f ( G , T ) gravity

Noether symmetry approach in $$f(\mathcal {G},T)$$ f ( G , T ) gravity

Generalized (2+1) dimensional black hole by Noether symmetry

Some exact solutions in f(𝒢,T) gravity via Noether symmetries

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