Non-Commutative Correction to Thin Shell Collapse in Reissner–Nordström Geometry

Sharif, M.; Abbas, G.

doi:10.1143/jpsj.81.044002

Cited by 6 publications

(5 citation statements)

References 33 publications

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“…After a straightforward but laborious calculations, we get the same relation for R as in (19). This verifies the fact that the solution ( 15) is the valid solution of the Einstein field equations with the charged anisotropic source.…”

Section: Properties Of the Modelsupporting

confidence: 72%

“…Inspired by the NC correction to BH physics, Oh and Park [18] explored the gravitational collapse of shell with smeared gravitational source in the NC Schwarzschild geometry. We have extended this work for NC Reissner-Nordström background [19]. Sun et al [20] studied gravitational collapse of spherically symmetric star in NC GR using spacetime quantization approach.…”

Section: Introductionmentioning

confidence: 99%

“…We have extended this work for the NC Reissner-Nordström background. [19] Sun et al [20] studied the gravitational collapse of a spherically symmetric star in NC GR using the spacetime quantization approach.…”

Section: Introductionmentioning

confidence: 99%

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Singularities of noncompact charged objects

Sharif

Abbas

2013

Chinese Phys. B

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We formulate a model of noncompact spherical charged objects in the framework of noncommutative field theory. The Einstein-Maxwell field equations are solved with charged anisotropic fluid. We choose the forms of mass and charge densities which belong to two parameter family of density distribution functions instead of densities as Gaussian width length. It is found that the corresponding densities and the Ricci scalar are singular at origin whereas the metric is nonsingular indicating a spacelike singularity. The numerical solution of the horizon equation implies that there are either two or one or no horizon depending on the mass. We also evaluate the Hawking temperature which implies that a black hole with two horizons is evaporated to an extremal black hole with one horizon.

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Section: Properties Of the Modelsupporting

confidence: 72%

Section: Introductionmentioning

confidence: 99%

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Singularities of noncompact charged objects

Sharif

Abbas

2013

Chinese Phys. B

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“…In particular, the curvature of any BH spacetime is analysed through geodesics around it to obtain a rich structure with conveying the characteristics of that particular spacetime geometry [1, 3,4]. In last few decades, several studies have been done concerning the non-commutative geometry in GR as an intrinsic property of spacetime which does not depend on curvature of spacetime and gained interest in context of approaching gravity at quantum level [5][6][7][8][9][10][11][12][13][14][15][16]. Following the non-commutative Heisenberg algebra [17], the non-commutative inspired geometry in GR can be interpreted as an uncertainty in the spatial coordinates defined by the commutation relation [x µ , x ν ] = iα µν , where α µν being an antisymmetric matrix [10,12,18,19].…”

Section: Introductionmentioning

confidence: 99%

Geodesic stability and quasinormal modes of non-commutative Schwarzschild black hole employing Lyapunov exponent

Giri,

Nandan,

Joshi

et al. 2022

Preprint

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We study the dynamics of test particle and stability of circular geodesics in the gravitational field of a non-commutative geometry inspired Schwarzschild black hole spacetime (NCSBH). The coordinate time Lyapunov exponent (λc) is crucial to investigate the stability of equatorial circular geodesics of massive and massless test particles. The stability or instability of circular orbits are discussed by analysing the variation of Lyapunov exponent with radius of these orbits for different values of non-commutative parameter (α). In the case of null circular orbits, the instability exponent is calculated and presented to discuss the instability of null circular orbits. Further, by relating parameters corresponding to null circular geodesics (i.e. angular frequency and Lyapunov exponent), the quasinormal modes (QNMs) for a massless scalar field perturbation in the eikonal approximation are evaluated, and also visualised by relating the real and imaginary parts. The nature of scalar field potential, by varying the non-commutative parameter (α) and angular momentum of perturbation (l), are also observed and discussed.

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“…Farook et al [18] have investigated the higher dimensional wormhole solutions in NC theory of gravity. Motivated by such NC correction to BHs, Sharif and Abbas [19] studied the thin shell collapse in NC Reissner-Nordström geometry. Banerjee and Gangopadhyay [20] derived the Komar energy and Sammar formula for NC Schwarzschild BH.…”

Section: Introductionmentioning

confidence: 99%

Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

Abbas

2014

Advances in High Energy Physics

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Few years ago, Setare [1] has investigated the Cardy-Verlinde formula of non-commutative black hole obtained by non-commutativity of coordinates. In this paper, we apply the same procedure to a non-commutative black hole obtained by the co-ordinate coherent approch. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal filed theory to its total energy and Casimir energy. In paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of non-commutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.as generalized Verlinde formula (commonly termed as Cardy-Verlinde formula). Recently, it has been investigated that this formula hold well for Reissner-Nordström de-Sitter black hole (BH) [3] and charged Kerr BH [4]. Birmingham and Mokhtari proved the validity of Birmingham and Mokhtari [5] proved the Verlinde formula for Taub-Bolt-Anti-de-Sitter BH. Setare and Jamil [6] discussed the Cardy-Verlinde formula for charged BTZ BH. Many authors [7]-[12] have proved the validity of Cardy-Verlinde for different BHs. The purpose of this paper is to investigate the validity of Cardy-Verlinde entropy formula for NC Schwarzschild BH.In classical general relativity (GR), the curvature singularity is such a point where physical description of the gravitational field is impossible. This problem can be removed in GR by taking into account the quantum mechanical treatment to the standard formulation of GR. Motivated by such reasoning, some BH solutions in non-commutative (NC) field theory have been derived. In these solutions, curvature singularity at origin is removed by de-Sitter core which is introduced due to NC nature of spacetime [13]. Ansoldi et al. [14] formulated the NC charged BHs solutions, this was extended to rotating non-commutative BHs case by Modesto and Nicollini [15]. Mann and Nicolini [16] have discussed the cosmological production of NC BHs. The first NC version of wormholes solution was investigated by Nicolini and Spallucci [17]. Farook et al. [18] have investigated the higher dimensional wormhole solutions in NC theory of gravity. Motivated by such NC correction to BHs, Sharif and Abbas [19] studied the thin shell collapse in NC Reissner-Nordström geometry. Banerjee and Gangopadhyay [20] derived the Komar energy and Sammar formula for NC Schwarzschild BH.Motivated by the recent development in NC theory of gravity, we have proved that the entropy of NC Schwarzschild BH horizon can be expressed in terms of Cardy-Verlinde formula. For this purpose, we have used the Setare and Jamil method [6]. The plan of the paper is as follows: In section 2, we briefly discussed the the thermodynamical relations of NC Schwarzschild BH and Cardy-Verlinde formula and proved that entropy of non-commutative Schwarzschild BH horizon in can be expressed in terms of Cardy-Verlinde formula. Section 3 is devoted to the concluded remarks of the work ...

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Non-Commutative Correction to Thin Shell Collapse in Reissner–Nordström Geometry

Cited by 6 publications

References 33 publications

Singularities of noncompact charged objects

Singularities of noncompact charged objects

Geodesic stability and quasinormal modes of non-commutative Schwarzschild black hole employing Lyapunov exponent

Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

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