Search

In this paper, we take into account the dilaton black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. At first, we consider the cosmological constant and nonlinear parameter as thermodynamic quantities which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature and Gibbs free energy in an extended phase space. We complete the analogy of the nonlinear dilaton black holes with Van der Waals liquid-gas system. We work in the canonical ensemble and hence we treat the charge of the black hole as an external fixed parameter. Moreover, we calculate the critical values of temperature, volume and pressure and show they depend on dilaton coupling constant as well as nonlinear parameter. We also investigate the critical exponents and find that they are universal and independent of the dilaton and nonlinear parameters, which is an expected result. {Finally, we explore the phase transition of nonlinear dilaton black holes by studying the Gibbs free energy of the system. We find that in case of $T>T_c$, we have no phase transition. When $T=T_c$, the system admits a second order phase transition, while for $T=T_{\rm f}

We explore the critical behavior of (n+1)-dimensional topological Born-Infeld-dilaton black holes in an extended phase space. We treat the cosmological constant and the Born-Infeld (BI) parameter as the thermodynamic pressure and BI vacuum polarization which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature, Gibbs free energy, and investigate the behaviour of these quantities. We also study the analogy of the van der Waals liquid-gas system with the Born-Infeld-dilaton black holes in canonical ensemble in which we can treat the black hole charge as a fixed external parameter. Moreover, we show that the critical values of pressure, temperature and volume are physical provided the coupling constant of dilaton gravity is less than one and the horizon is sphere. Finally, we calculate the critical xponents and show that although thermodynamic quantities depend on the dilaton oupling constant, BI parameter and the dimension of the spacetime, they are universal and are independent of metric parameters., Comment: 14 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:1611.00590

We investigate the critical behavior of an $(n+1)$-dimensional topological dilaton black holes, in an extended phase space in both canonical and grand-canonical ensembles, when the gauge field is in the form of power-Maxwell field. In order to do this we introduce for the first time the counterterms that remove the divergences of the action in dilaton gravity for the solutions with curved boundary. Using the counterterm method, we calculate the conserved quantities and the action and therefore Gibbs free energy in both the canonical and grand-canonical ensembles. We treat the cosmological constant as a thermodynamic pressure, and its conjugate quantity as a thermodynamic volume. In the presence of power-Maxwell field, we find an analogy between the topological dilaton black holes with van der Walls liquid-gas system in all dimensions provided the dilaton coupling constant $\alpha$ and the power parameter $p$ are chosen properly. Interestingly enough, we observe that the power-Maxwell dilaton black holes admit the phase transition in both canonical and grand-canonical ensembles. This is in contrast to RN-AdS, Einstein-Maxwell-dilaton and Born-Infeld-dilaton black holes, which only admit the phase transition in the canonical ensemble. Besides, we calculate the critical quantities and show that they depend on $\alpha$, $n$ and $p$. Finally, we obtain the critical exponents in two ensembles and show that they are independent of the model parameters and have the same values as mean field theory., Comment: 19 pages, 18 figures

We construct a new class of charged rotating black brane solutions in the presence of logarithmic nonlinear electrodynamics with complete set of the rotation parameters in arbitrary dimensions. The topology of the horizon of these rotating black branes are flat, while, due to the presence of the dilaton field the asymptotic behaviour of them are neither flat nor (anti)-de Sitter [(A)dS]. We investigate the physical properties of the solutions. The mass and angular momentum of the spacetime are obtained by using the counterterm method inspired by AdS/CFT correspondence. We derive temperature, electric potential and entropy associated with the horizon and check the validity of the first law of thermodynamics on the black brane horizon. We study thermal stability of the solutions in both canonical and grand canonical ensemble and disclose the effects of the rotation parameter, nonlinearity of electrodynamics and dilaton field on the thermal stability conditions. We find the solutions are thermally stable for $\alpha<1$, while for $\alpha>1$ the solutions may encounter an unstable phase where $\alpha$ is dilaton-electromagnetic coupling constant., Comment: 15 pages, 11 figures

In this paper, we construct a new class of topological black hole Lifshitz solutions in the presence of nonlinear exponential electrodynamics for Einstein-dilaton gravity. We show that the reality of Lifshitz supporting Maxwell matter fields exclude the negative horizon curvature solutions except for the asymptotic AdS case. Calculating the conserved and thermodynamical quantities, we obtain a Smarr type formula for the mass and confirm that thermodynamics first law is satisfied on the black hole horizon. Afterward, we study the thermal stability of our solutions and figure out the effects of different parameters on the stability of solutions under thermal perturbations. Next, we apply the gauge/gravity duality in order to calculate the ratio of shear viscosity to entropy for a three-dimensional hydrodynamic system by using the pole method. Furthermore, we study the behavior of holographic conductivity for two-dimensional systems such as graphene. We consider linear Maxwell and nonlinear exponential electrodynamics separately and disclose the effect of nonlinearity on holographic conductivity. We indicate that holographic conductivity vanishes for $z>3$ in the case of nonlinear electrodynamics while it does not in the linear Maxwell case. Finally, we solve perturbative additional field equations numerically and plot the behaviors of real and imaginary parts of conductivity for asymptotic AdS and Lifshitz cases. We present experimental results match with our numerical ones., Comment: 31 pages, 16 figures (some figures include two subfigures). V2: some typos corrected, some references added

In this paper, we present a new class of higher dimensional exact topological black hole solutions of the Brans-Dicke theory in the presence of a power-law Maxwell field as the matter source. For this aim, we introduce a conformal transformation which transforms the Einstein-dilaton-power-law Maxwell gravity Lagrangian to the Brans-Dicke-power-law Maxwell theory one. Then, by using this conformal transformation, we obtain the desired solutions. Next, we study the properties of the solutions and conditions under which we have black holes. Interestingly enough, we show that there is a cosmological horizon in the presence of a negative cosmological constant. Finally, we calculate the temperature and charge and then by calculating the Euclidean action, we obtain the mass, the entropy and the electromagnetic potential energy. We find that the entropy does not respect the area law, and also the conserved and thermodynamic quantities are invariant under conformal transformation. Using these thermodynamic and conserved quantities, we show that the first law of black hole thermodynamics is satisfied on the horizon., Comment: 10 pages (two columns format), 10 figures, some references added, titles of references added

We explore an effective supergravity action in the presence of a massless gauge field which contains the Gauss-Bonnet term as well as a dilaton field. We construct a new class of black brane solutions of this theory with the Lifshitz asymptotic by fixing the parameters of the model such that the asymptotic Lifshitz behavior can be supported. Then we construct the well-defined finite action through the use of the counterterm method. We also obtain two independent constants along the radial coordinate by combining the equations of motion. Calculations of these two constants at infinity through the use of the large-$r$ behavior of the metric functions show that our solution respects the no-hair theorem. Furthermore, we combine these two constants in order to get a constant $C$ which is proportional to the energy of the black brane. We calculate this constant at the horizon in terms of the temperature and entropy, and at large-$r$ in terms of the geometrical mass. By calculating the value of the energy density through the use of the counterterm method, we obtain the relation between the energy density, the temperature, and the entropy. This relation is the generalization of the well-known Smarr formula for AdS black holes. Finally, we study the thermal stability of our black brane solution and show that it is stable under thermal perturbations., Comment: 11 pages, version to be published in Phys. Rev. D

In this paper, we construct a new class of charged rotating dilaton black brane solutions, with complete set of rotation parameters, which is coupled to a nonlinear Maxwell field. The Lagrangian of the matter field has the form of the power-law Maxwell field. We study the causal structure of the spacetime and its physical properties in ample details. We also compute thermodynamic and conserved quantities of the spacetime such as the temperature, entropy, mass, charge, and angular momentum. We find a Smarr-formula for the mass and verify the validity of the first law of thermodynamics on the black brane horizon. Finally, we investigate the thermal stability of solutions in both canonical and grand-canonical ensembles and disclose the effects of dilaton field and nonlinearity of Maxwell field on the thermal stability of the solutions. We find that for $\alpha \leq 1$, charged rotating black brane solutions are thermally stable independent of the values of the other parameters. For $\alpha>1$, the solutions can encounter an unstable phase depending on the metric parameters., Comment: 15 pages, 14 figures. We have revised the text to remove the overlaps

The energy density of the holographic dark energy is based on the area law of entropy, and thus any modification of the area law leads to a modified holographic energy density. Inspired by the entropy expression associated with the apparent horizon of a Friedmann-Robertson-Walker (FRW) Universe in DGP braneworld, we propose a new model for the holographic dark energy in the framework of DGP brane cosmology. We investigate the cosmological consequences of this new model and calculate the equation of state parameter by choosing the Hubble radius, $L = H^{-1}$, as the system's IR cutoff. Our study show that, due to the effects of the extra dimension (bulk), the identification of IR-cutoff with Hubble radius, can reproduce the present acceleration of the Universe expansion. This is in contrast to the ordinary holographic dark energy in standard cosmology which leads to the zero equation of state parameter in the case of choosing the Hubble radius as system's IR cutoff in the absence of interaction between dark matter and dark energy., Comment: 11 pages

In this paper, we construct a new class of analytic topological Lifshitz black holes with constant curvature horizon in the presence of power-law Maxwell field in four and higher dimensions. We find that in order to obtain these exact Lifshitz solutions, we need a dilaton and at least three electromagnetic fields. Interestingly enough, we find that the reality of the charge of the electromagnetic field which is needed for having solutions with curved horizon rules out black holes with hyperbolic horizon. Next, we study the thermodynamics of these nonlinear charged Lifshitz black holes with spherical and flat horizons by calculating all the conserved and thermodynamic quantities of the solutions. Furthermore, we obtain a generalized Smarr formula and show that the first law of thermodynamics is satisfied. We also perform a stability analysis in both canonical and grand-canonical ensemble. We find that the solutions are thermally stable in a proper ranges of the metric parameters. Finally, we comment on the dynamical stability of the obtained solutions under perturbations in four dimensions., Comment: 11 pages, 11 figures. A discussion about general nonlinear electrodynamic Lagrangians has been added. Dynamical stability discussions have been added. A Ref. has been added and a Ref. has been corrected

In this paper, we investigate the critical behavior of charged black holes of Einstein-Maxwell-dilaton gravity in the presence of two Liouville-type potentials which make the solution asymptotically neither flat nor AdS and has a parameter $% \Lambda $ treated as a thermodynamic quantity that can vary. We obtain a Smarr-type relation for charged dilatonic black holes and find out that the volume is different from the geometrical volume. We study the analogy of the Van der Waals liquid-gas system with the charged dilatonic black hole system while we treat the black hole charge as a fixed external parameter. Moreover, we show that the critical values for pressure, temperature and volume are physical provided the coupling constant of dilaton gravity is less than one and the horizon is sphere. Finally, we calculate the critical exponents and show that they are universal and are independent of the details of the system although the thermodynamic quantities depend on the dilaton parameter and the dimension of the spacetime., Comment: 12 pages, 4 figures

In this paper, we investigate the thermodynamics of hyperscaling violating Lifshitz black branes in the presence of a nonlinear massless electromagnetic field. We, first, obtain analytic nonlinear charged black brane solutions with hyperscaling violating factor in dilaton gravity and give the condition on the parameters of the metric for having black brane solutions. Second, we introduce the appropriate finite action in grand-canonical and canonical ensembles for nonlinear electromagnetic field. Next, by generalizing the counterterm method for the asymptotic Lifshitz spacetimes with hyperscaling violating factor, we calculate the energy density of our solutions. Then, we present a relation between the energy density and the thermodynamic quantities, electric potential, charge density, temperature and entropy density. This relation is the generalization of Smarr formula for anti-de Sitter black branes and charged Lifshiz solutions. Finally, we perform a stability analysis in both the canonical and grand-canonical ensemble. We show that the nonlinearity of electromagnetic field can make the solutions unstable in grand-canonical ensemble., Comment: 16 pages, one figure. arXiv admin note: text overlap with arXiv:1209.3946 by other authors

In this paper, we extend the study on the nonlinear power-law Maxwell field to dilaton gravity. We introduce the $(n+1)$-dimensional action in which gravity is coupled to a dilaton and power-law nonlinear Maxwell field, and obtain the field equations by varying the action. We construct a new class of higher dimensional topological black hole solutions of Einstein-dilaton theory coupled to a power-law nonlinear Maxwell field and investigate the effects of the nonlinearity of the Maxwell source as well as the dilaton field on the properties of the spacetime. Interestingly enough, we find that the solutions exist provided one assumes three Liouville-type potentials for the dilaton field, and in case of the Maxwell field one of the Liouville potential vanishes. After studying the physical properties of the solutions, we compute the mass, charge, electric potential and temperature of the topological dilaton black holes. We also study thermodynamics and thermal stability of the solutions and disclose the effects of the dilaton field and the power-law Maxwell field on the thermodynamics of these black holes. Finally, we comment on the dynamical stability of the obtained solutions in four-dimensions., Comment: 11 pages, 11 figures, 2 column format. arXiv admin note: text overlap with arXiv:0709.3619

Many dark energy (DE) models have been proposed, in recent years, to explain acceleration of the Universe expansion. It seems necessary to discriminate the various DE models in order to check the viability of each model. Statefinder diagnostic is a useful method which can differentiate various DE models. In this paper, we investigate the statefinder diagnosis parameters for the holographic dark energy (HDE) model in two cosmological setup. First, we study statefinder diagnosis for HDE in the context of flat Friedmann-Robertson-Walker (FRW) Universe in Einstein gravity. Then, we extend our study to the DGP braneworld framework. As system's IR cutoff we chose the Hubble radius and the Granda-Oliveros cutoff inspired by Ricci scalar curvature. We plot the evolution of statefinder parameres $\{r,s\}$ in terms of the redshift parameter $z$. We also compare the results with those obtained for statefinder diagnosis parameters of other DE models, in particular with $\Lambda$CDM model., Comment: 14 pages

We consider the holographic dark energy (HDE) model in the framework of DGP braneworld with Granda-Oliveros infrared (IR) cutoff, $L=(\alpha \dot{H}+\beta H^2)^{-1/2}$. With this choice for IR cutoff, we are able to derive evolution of the cosmological parameters such as the equation of state and the deceleration parameters, $w$ and $q$, as the functions of the redshift parameter $z$. As far as we know, most previous models of HDE presented in the literatures, do not gives analytically $\omega=\omega(z)$ and $q=q(z)$. We plot the evolution of these parameters versus $z$ and discuss that the results are compatible with the recent observations. With suitably choosing the parameters, this model can exhibit a transition from deceleration to the acceleration around $z\approx 0.6$. Then, we suggest a correspondence between the quintessence and tachyon scalar fields and HDE in the framework of DGP braneworld. This correspondence allows us to reconstruct the evolution of the scalar fields and the scalar potentials. We also investigate stability of the presented model by calculating the squared sound speed, $v^2_s$, whose sign determines the stability of the model. Our study shows that $v^2_s$ could be positive provided the parameters of the model are chosen suitably. In particular, for $\alpha>1$, $\beta>0$, and $\alpha<1$, $\beta<0$, we have $v^2_s>0$ during the history of the universe, and so the stable dark energy dominated universe can be achieved. This is in contrast to the HDE in standard cosmology, which is unstable against background perturbations and so cannot lead to a stable dark energy dominated universe., Comment: 13 pages

In this paper, we introduce the counterterms that remove the non-logarithmic divergences of the action in third order Lovelock gravity for static spacetimes. We do this by defining the cosmological constant in such a way that the asymptotic form of the metric have the same form in Lovelock and Einstein gravities. Thus, we employ the counterterms of Einstein gravity and show that the power law divergences of the action of Lovelock gravity for static spacetimes can be removed by suitable choice of coefficients. We find that the dependence of these coefficients on the dimension in Lovelock gravity is the same as in Einstein gravity. We also introduce the finite energy-momentum tensor and employ these counterterms to calculate the finite action and mass of static black hole solutions of third order Lovelock gravity. Next, we calculate the thermodynamic quantities and show that the entropy calculated through the use of Gibbs-Duhem relation is consistent with the obtained entropy by Wald's formula. Furthermore, we find that in contrast to Einstein gravity in which there exists no uncharged extreme black hole, third order Lovelock gravity can have these kind of black holes. Finally, we investigate the stability of static charged black holes of Lovelock gravity in canonical ensemble and find that small black holes show a phase transition between very small and small black holes, while the large ones are stable., Comment: arXiv admin note: text overlap with arXiv:1008.0102 by other authors