In this paper, the charged three-dimensional Einstein's theory coupled to a dilatonic field has been considered in the rainbow gravity. The dilatonic potential has been written as the linear ...combination of two Liouville-type potentials. Four new classes of charged dilatonic rainbow black hole solutions, as the exact solution to the coupled field equations of the energy dependent space time, have been obtained. Two of them are correspond to the Coulomb's electric field and the others are consequences of a modified Coulomb's law. Total charge and mass as well as the entropy, temperature and electric potential of the new charged black holes have been calculated in the presence of rainbow functions. Although the thermodynamic quantities are affected by the rainbow functions, it has been found that the first law of black hole thermodynamics is still valid for all of the new black hole solutions. At the final stage, making use of the canonical ensemble method and regarding the black hole heat capacity, the thermal stability or phase transition of the new rainbow black hole solutions have been analyzed.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Two new families of nonlinearly charged and asymptotically anti-de Sitter (AdS) rainbow black holes have been introduced, as the exact solutions to the coupled electromagnetic and gravitational field ...equations, in massive gravity theory and in the presence of power-law nonlinear electrodynamics. The conserved and thermodynamic quantities such as black hole mass, charge, temperature, entropy and electric potential have been calculated from geometric and thermodynamic approaches. Despite the fact that some of them receive corrections from rainbow functions and nonlinear electrodynamics, it has been proved that they fulfill the first law of black hole thermodynamics. Thermal stability of the black holes has been studied by use of the canonical ensemble and geometrical thermodynamics methods, separately. Regarding the black hole heat capacity and thermodynamic Ricci scalars, the points of type-one and type-two phase transitions and the conditions under which the black holes remain locally stable have been determined. Also, global stability of the novel rainbow black holes has been investigated from the viewpoint of the grand canonical ensemble. Through calculation of Gibbs free energy of the black holes, the points of Hawking-Page phase transition and the size of the black holes which are globally stable or in the radiative phase have been determined.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In the present work, we have studied the thermodynamical properties of black holes arising as the solutions of the four-dimensional dilaton gravity coupled to Maxwell's electrodynamics in gravity's ...rainbow. This theory allows three classes of asymptotically non-flat and non-AdS black hole solutions. We showed that the self-interacting scalar function, as the solution to the scalar field equation, can be written as the linear combination of three Liouville-type potentials. The thermodynamical quantities are identified and in particular, a generalized Smarr formula is derived. It is shown that, although the thermodynamic quantities are affected by the rainbow functions, the validity of the black hole thermodynamical first law is supported. The thermodynamic stability of the solutions have been analyzed through the black hole heat capacity. We have shown that, even in the presence of the rainbow functions, the black holes can be locally stable in the sense that there exists a range of the horizon radiuses for which the heat capacity is positive.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In this paper, the linearly charged three-dimensional Einstein’s theory coupled to a dilatonic field has been considered. It has been shown that the dilatonic potential must be considered in a form ...of generalized Liouville-type potential. Two new classes of charged dilatonic black hole solutions, as the exact solutions to the Einstein-Maxwell-dilaton (EMd) gravity, have been obtained and their properties have been studied. The conserved charge and mass related to both of the new EMd black holes have been calculated. Through comparison of the thermodynamical extensive quantities (i.e., temperature and entropy) obtained from both, the geometrical and the thermodynamical methods, the validity of first law of black hole thermodynamics has been investigated for both of the new black holes we just obtained. At the final stage, making use of the canonical ensemble method and regarding the black hole heat capacity, the thermal stability or phase transition of the new black hole solutions have been analyzed. It has been shown that there is a specific range for the horizon radius in such a way that the black holes with the horizon radius in that range are locally stable. Otherwise, they are unstable and may undergo type one or type two phase transitions to be stabilized.
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Thermodynamics and thermal stability of novel charged dilaton black holes have been analyzed in the presence of the exponential nonlinear electrodynamics. It has been found that the scalar field can ...be written as the linear combination of two Liouville-type potentials. Three new classes of nonlinearly charged dilatonic black holes have been obtained as the exact solutions to the coupled scalar, electromagnetic, and gravitational field equations. The impacts of nonlinear electrodynamics on the conserved and thermodynamic quantities of the new black hole solutions have been calculated. It has been illustrated that the first law of black hole thermodynamics is valid for either of the new black hole solutions. A thermal stability or phase transition analysis has been performed making use of the canonical ensemble method. The points of type-1 and type-2 phase transitions as well as the ranges at which the new nonlinearly charged dilatonic black holes are locally stable have been determined.
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In this work, the three-dimensional nonlinearly charged black holes have been considered with a power-law modified electromagnetic theory. The black hole solutions to Einstein’s three-dimensional ...field equations with a negative cosmological constant have been constructed in the presence of power-law nonlinear electrodynamics. Through the physical and mathematical interpretation of the solutions, a new class of asymptotically anti–de Sitter (AdS) black hole solutions has been introduced. The area law, surface gravity, and Gauss’s law are utilized to obtain the entropy, temperature, and electric charge of the new AdS black holes, respectively. The quasilocal mass of the solutions has been calculated based on the counterterm method. A Smarr-type formula for the mass as a function of entropy and charge has been obtained. It has been shown that the thermodynamical quantities satisfy the first law of thermodynamics for the new AdS black holes. Also, it has been found that in order for the Smarr mass formula to be compatible with the first law of black hole thermodynamics, the cosmological parameter Λ should be treated as a thermodynamical variable and the generalized first law of thermodynamics has been introduced. Through the canonical ensemble method, the black hole remnant or phase transitions have been investigated regarding the black hole heat capacity. It has been found that the AdS black hole solutions we just obtained are thermodynamically stable.
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In this work, thermodynamic properties of the three-dimensional charged dilatonic black holes are considered in the presence of Born-Infeld nonlinear electrodynamics. The exact nonlinearly charged ...black hole solutions to the coupled Einstein-Born-Infeld three-dimensional field equations in the presence of a dilatonic scalar field are constructed. Some new classes of nonlinearly charged dilatonic black hole solutions are distinguished according to different values of the parameters in the theory. The thermodynamics of all of the new Einstein-Born-Infeld-dilaton black holes are studied separately. We show that the thermodynamic quantities satisfy the first law of black hole thermodynamics. Through the canonical ensemble method and noting the black hole heat capacity, we analyze the stability and thermodynamic phase transitions of all of the new Einstein-Born-Infeld-dilaton black holes.
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In this work, we explore the charged black holes with the power-law modified electromagnetic theory in a three-dimensional energy dependent space-time. Through exact solution of the field equations, ...we introduce a new class of nonlinearly charged black holes which are asymptotically anti-de Sitter (AdS). The black hole entropy, temperature and electric potential are calculated from the geometrical approaches. The counterterm method and Gauss's electric law are utilized for calculating the black hole mass and electric charge, respectively. By use of the Smarr formula, which states the black hole mass as the function of thermodynamic extensive parameters, we prove the validity of the first law of thermodynamics for the new AdS black holes. By use of the canonical ensemble method, the black hole remnant or phase transitions are investigated regarding the signature of black hole heat capacity. We show that the AdS black hole solutions, we just obtained, are thermodynamically stable if their horizon radii are greater than a minimum value. Then, by considering the black hole thermal fluctuations, we examine the quantum gravitational effects on the thermodynamic properties of the new AdS black holes. We prove that, when the thermal fluctuations are taken into account, the thermodynamical first law is no longer valid. Also, the thermal stability of the black holes gets some corrections.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In this paper, the three-dimensional Einstein–Maxwell theory in the presence of a dilatonic scalar field has been studied. It has been shown that the dilatonic potential must be considered as the ...linear combination of two Liouville-type potentials. Two new classes of charged dilatonic BTZ black holes, as the exact solutions to the coupled scalar, vector and tensor field equations, have been obtained and their properties have been studied. The conserved charge and mass of the new black holes have been calculated, making use of the Gauss's law and Abbott–Deser proposal, respectively. Through comparison of the thermodynamical extensive quantities (i.e. temperature and entropy) obtained from both, the geometrical and the thermodynamical methods, the validity of the first law of black hole thermodynamics has been confirmed for both of the new black holes we just obtained. A black hole thermal stability or phase transition analysis has been performed, making use of the canonical ensemble method. Regarding the black hole heat capacity, it has been found that for either of the new black hole solutions there are some specific ranges in such a way that the black holes with the horizon radius in these ranges are locally stable. The points of type one and type two phase transitions have been determined. The black holes, with the horizon radius equal to the transition points are unstable. They undergo type one or type two phase transitions to be stabilized.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The action of three-dimensional charged Einstein-dilaton gravity theory has been obtained from that of scalar-tensor modified gravity theory by utilizing the suitable conformal transformations. The ...field equations of the Einstein-dilaton gravity coupled to the power Maxwell nonlinear electrodynamics have been solved and two new classes of static and spherically symmetric charged dilatonic black holes, as the exact solutions to the coupled scalar, electromagnetic and gravitational field equations, have been obtained. Also, the dilaton potential has been written as the linear combination of two Liouville-type potentials. The black hole conserved charges and thermodynamic quantities have been calculated by utilizing the geometrical and thermodynamical methods, separately. The compatibility of the results obtained from these two alternative approaches confirms the validity of the first law of black hole thermodynamics for both of the new black hole solutions in the Einstein frame. A black hole stability or phase transition analysis has been performed in the context of the canonical ensemble. By calculating the black hole heat capacity, with the black hole charge as a constant, the type one and type two phase transition points have been determined. Also, the ranges of the black hole horizon radii at which the Einstein black holes are thermally stable have been identified for both of the new black hole solutions. Then making use of the inverse conformal transformations, two new classes of the scalar-tensor black holes have been obtained from their Einstein frame counterparts. The thermodynamic properties and thermal stability of the new scalar-tensor black holes have been investigated. It has been found that the new charged black holes have the same thermodynamic behaviors in both of the Einstein and Jordan frames.
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