Exact solutions of three-dimensional black holes: Einstein gravity versus F(R) gravity

Hendi, S. H.; Panah, B. Eslam; Saffari, Reza

doi:10.1142/s0218271814500886

Cited by 89 publications

(81 citation statements)

References 36 publications

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“…Interesting properties of various nonlinear electrodynamics have been studied before by many authors . One of the special classes of the nonlinear electrodynamic sources is the power-law Maxwell invariant (PMI), of which the Lagrangian is an arbitrary power of the Maxwell Lagrangian [26][27][28][29][30]. It is notable that this Lagrangian is invariant under the conformal transformation g μν −→ 2 g μν and A μ −→ A μ , where g μν and A μ are the metric tensor and the electromagnetic potential, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Geometrical thermodynamics and P–V criticality of the black holes with power-law Maxwell field

et al. 2017

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We study the thermodynamical structure of Einstein black holes in the presence of power Maxwell invariant nonlinear electrodynamics for two different cases. The behavior of temperature and conditions regarding the stability of these black holes are investigated. Since the language of geometry is an effective method in general relativity, we concentrate on the geometrical thermodynamics to build a phase space for studying thermodynamical properties of these black holes. In addition, taking into account the denominator of the heat capacity, we use the proportionality between cosmological constant and thermodynamical pressure to extract the critical values for these black holes. Besides, the effects of the variation of different parameters on the thermodynamical structure of these black holes are investigated. Furthermore, some thermodynamical properties such as the volume expansion coefficient, speed of sound, and isothermal compressibility coefficient are calculated and some remarks regarding these quantities are given.

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Section: Introductionmentioning

confidence: 99%

“…This model is considerably richer than Maxwell theory, and in a special case (unit power), it reduces to a linear Maxwell field (see Refs. [26][27][28][29][30], for more details). The studies on the black object solutions coupled to the PMI field have got a lot of attention in the past decade [31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Geometrical thermodynamics and P–V criticality of the black holes with power-law Maxwell field

et al. 2017

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“…Also, it is consistent with neither Mach's principle nor Dirac's large number hypothesis [11,12]. Thus, cosmologists explored various alternatives for gravitational fields [13][14][15][16][17][18][19][20][21][22]. The pioneering studies of scalar-tensor theory were done by Brans and Dicke [23].…”

Section: Introductionmentioning

confidence: 99%

Phase transition of charged Black Holes in Brans–Dicke theory through geometrical thermodynamics

et al. 2016

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In this paper, we take into account black hole solutions of Brans-Dicke-Maxwell theory and investigate their stability and phase transition points. We apply the concept of geometry in thermodynamics to obtain phase transition points and compare its results with those, calculated in the canonical ensemble through heat capacity. We show that these black holes enjoy second order phase transitions. We also show that there is a lower bound for the horizon radius of physical charged black holes in Brans-Dicke theory, which originates from restrictions of positivity of temperature. In addition, we find that employing a specific thermodynamical metric in the context of geometrical thermodynamics yields divergencies for the thermodynamical Ricci scalar in places of the phase transitions. It will be pointed out that due to the characteristic behavior of the thermodynamical Ricci scalar around its divergence points, one is able to distinguish the physical limitation point from the phase transitions. In addition, the free energy of these black holes will be obtained and its behavior will be investigated. It will be shown that the behavior of the free energy in the place where the heat capacity diverges demonstrates second order phase transition characteristics.

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“…In the case of s = 3 4 , one can obtain a well-known metric which is called conformally invariant Maxwell solution [26], such as…”

Section: Metric and Geodesic Equationsmentioning

confidence: 99%

Study of geodesic motion in a (2+1)-dimensional charged BTZ black hole

Soroushfar¹,

Saffari²,

Jafari³

2016

Phys. Rev. D

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This study is purposed to derive the equation of motion for geodesics in vicinity of spacetime of a (2 + 1)-dimensional charged BTZ black hole. In this paper, we solve geodesics for both massive and massless particles in terms of Weierstrass elliptic and Kleinian sigma hyper-elliptic functions.Then we determine different trajectories of motion for particles in terms of conserved energy and angular momentum and also using effective potential. * Electronic address: rsk@guilan.ac.ir 1

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Exact solutions of three-dimensional black holes: Einstein gravity versus F(R) gravity

Cited by 89 publications

References 36 publications

Geometrical thermodynamics and P–V criticality of the black holes with power-law Maxwell field

Geometrical thermodynamics and P–V criticality of the black holes with power-law Maxwell field

Phase transition of charged Black Holes in Brans–Dicke theory through geometrical thermodynamics

Study of geodesic motion in a (2+1)-dimensional charged BTZ black hole

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