Liouville-type Potential Research Articles

Odd dimensional nonlocal Liouville conformal field theories

We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a mathcal{Q} -curvature background, and an exponential Liouville-type potential. We study the classical and quantum properties of these theories including the finite entanglement entropy part of the sphere partition function F, the boundary conformal anomaly and vertex operators’ correlation functions. We derive the analogue of the even-dimensional DOZZ formula and its semi-classical approximation.

Quasinormal modes of charged fermions in linear dilaton black hole spacetime: exact frequencies

We study charged massless fermionic perturbations in the background of $4$-dimensional linear dilaton black holes in Einstein-Maxwell-dilaton theory with double Liouville-type potentials. We present the analytical fermionic quasinormal modes, whose Dirac equations are solved in terms of hypergeometric functions. We also discuss the stability of these black holes under the charged fermionic perturbations.

Dilaton black holes with logarithmic source in gravity’s rainbow

Starting from the suitable action of four-dimensional Einstein gravity, which is coupled to a scalar dilaton field and logarithmic nonlinear electrodynamics, the related field equations have been solved in a spherically symmetric and energy-dependent spacetime. It has been found that the scalar potential, as the exact solution of the scalar field equations, must be written as the linear combination of two Liouville-type potentials. Three families of novel exact black holes have been introduced as the exact solutions to the gravitational equations, which are asymptotically non-flat and non-AdS. It has been illustrated that our solutions, recover their corresponding quantities in the Einstein–Maxwell-dilaton gravity theory when the nonlinearity parameter of electrodynamics is chosen very large. The thermodynamic and conserved quantities of the black holes have been calculated under the influence of the rainbow function. Then, through calculation of the Smarr mass formula, we have shown that the first law of black hole thermodynamics remain valid for all of the new dilatonic black holes. Thermal stability or phase transition of the black holes have been investigated by use of the canonical ensemble and thermodynamic geometry approaches, separately. By comparison of the results of these two alternative approaches, it has been found that they lead to the same results provided that the thermodynamic metric of HPEM is used.

A new black hole solution in dilaton gravity inspired by power-law electrodynamics

In this work, a new class of slowly rotating black hole solutions in dilaton gravity has been obtained where dilaton field is coupled with nonlinear Maxwell invariant. The background space–time is a stationary axisymmetric geometry. Here, it has been shown that the dilaton potential can be written in the form of generalized three Liouville-type potentials. In the presence of these three Liouville-type dilaton potentials, the asymptotic behavior of the obtained solutions is neither flat nor (A)dS. One bizarre property of the electric field is that the electric field goes to zero when [Formula: see text] and diverges at [Formula: see text]. We show the validity of the first law of thermodynamics in thermodynamic investigations. The local and global thermodynamical stability are investigated through the use of heat capacity and Gibbs free energy. Also, the bounded, phase transition and the Hawking–Page phase transition points as well as the ranges of black hole stability have been shown in the corresponding diagrams. From these diagrams, we can say that the presence of the dilaton field makes the solutions to be locally stable near origin and vanishes the global stability of our solutions. In final thermodynamics analysis, we obtain the Smarr formula for our solution. We will show that the presence of dilaton field brings a new term in the Smarr formula. Also, we find that the dilaton field makes the black hole (AdS) mass to decrease for every fix values of [Formula: see text] (entropy).

Thermodynamics of scalar-tensor-Maxwell black holes

The action of the charged Einstein-dilaton gravity theory is obtained from that of the scalar-tensor gravity theory by use of the transformations defined as $ g_{\mu\nu}\rightarrow \Omega^{2}g_{\mu\nu}$ and $ A_{\mu}\rightarrow A_{\mu}$. It is shown that, under these conformal transformations, the Lagrangian of Maxwell’s electrodynamics remains invariant in four-dimensional space-times. The related field equations are solved in the framework of Einstein-dilaton theory, and the dilatonic potential is obtained as a linear combination of three Liouville-type potentials. Two classes of novel charged black holes are identified as the exact solution to the field equations of the Einstein-Maxwell-dilaton theory. We calculate the conserved and thermodynamic quantities of dilaton black holes and show that the first law of black hole thermodynamics is valid in its standard form. Also, the thermodynamic stability or the phase transition of dilaton black holes is analyzed by use of the canonical ensemble method. Then, making use of the inverse conformal transformations, two classes of charged scalar-tensor black holes are obtained from their Einstein-dilaton counterparts and their thermodynamic properties as well as thermodynamic phase transitions are investigated.

Nonlinearly charged scalar-tensor black holes in ( 2+1 ) dimensions

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.

Thermodynamics of novel charged dilaton black holes in gravity's rainbow

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.

Thermodynamic properties of dilaton black holes with nonlinear electrodynamics

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.

Weyl transformation and regular solutions in a deformed Jackiw–Teitelboim model

We revisit a deformed Jackiw–Teitelboim model with a hyperbolic dilaton potential, constructed in the preceding work [arXiv:1701.06340]. Several solutions are discussed in a series of the subsequent papers, but all of them are pathological because of a naked singularity intrinsic to the deformation. In this paper, by employing a Weyl transformation to the original deformed model, we consider a Liouville-type potential with a cosmological constant term. Then regular solutions can be constructed with coupling to a conformal matter by using SL(2) transformations. For a black hole solution, the Bekenstein–Hawking entropy is computed from the area law. It can also be reproduced by evaluating the boundary stress tensor with an appropriate local counter-term (which is essentially provided by a Liouville-type potential).

Liouville conformal field theories in higher dimensions

We consider a generalization of the two-dimensional Liouville conformal field theory to any number of even dimensions. The theories consist of a log-correlated scalar field with a background mathcal{Q} -curvature charge and an exponential Liouville-type potential. The theories are non-unitary and conformally invariant. They localize semiclassically on solutions that describe manifolds with a constant negative mathcal{Q} -curvature. We show that CT is independent of the mathcal{Q} -curvature charge and is the same as that of a higher derivative scalar theory. We calculate the A-type Euler conformal anomaly of these theories. We study the correlation functions, derive an integral expression for them and calculate the three-point functions of light primary operators. The result is a higher-dimensional generalization of the two-dimensional DOZZ formula for the three-point function of such operators.

Thermodynamics of new black hole solutions in the Einstein–Maxwell-dilaton gravity

In the present work, thermodynamics of the new black hole solutions to the four-dimensional Einstein–Maxwell-dilaton gravity theory have been studied. The dilaton potential, as the solution to the scalar field equations, has been constructed out by a linear combination of three Liouville-type potentials. Three new classes of charged dilatonic black hole solutions, as the exact solutions to the coupled equations of gravitational, electromagnetic and scalar fields, have been introduced. The conserved charge and mass of the new black holes have been calculated by utilizing Gauss's electric law and Abbott–Deser mass proposal, respectively. Also, the temperature, entropy and the electric potential of these new classes of charged dilatonic black holes have been calculated, making use of the geometrical approaches. Through a Smarr-type mass formula, the intensive parameters of the black holes have been calculated and validity of the first law of black hole thermodynamics has been confirmed. A thermal stability or phase transition analysis has been performed, making use of the canonical ensemble method. The heat capacity of the new black holes has been calculated and the points of type one- and type two-phase transitions as well as the ranges at which the new charged dilatonic black holes are locally stable have been determined, precisely.

Thermal fluctuations of dilaton black holes in gravity's rainbow

In this work, thermodynamics and phase transition of some new dilaton black hole solutions have been explored in the presence of the rainbow functions. By introducing an energy dependent space time, the dilaton potential has been obtained as the linear combination of two Liouville-type potentials and three new classes of black hole solutions have been constructed. The conserved and thermodynamic quantities of the new dilaton black holes have been calculated in the energy dependent space times. It has been shown that, even if some of the thermodynamic quantities are affected by the rainbow functions, the thermodynamical first law still remains valid. Also, the impacts of rainbow functions on the stability or phase transition of the new black hole solutions have been investigated. Finally, the quantum gravitational effects on the thermodynamics and phase transition of the solutions have been studied through consideration of the thermal fluctuations.

Thermodynamic properties of charged three-dimensional black holes in the scalar-tensor gravity theory

Making use of the suitable transformation relations, the action of three-dimensional Einstein-Maxwell-dilaton gravity theory has been obtained from that of scalar-tensor modified gravity theory coupled to the Maxwell's electrodynamics as the matter field. Two new classes of the static three-dimensional charged dilatonic black holes, as the exact solutions to the coupled scalar, electromagnetic and gravitational field equations, have been obtained in the Einstein frame. Also, it has been found that the scalar potential can be written in the form of a generalized Liouville-type potential. The conserved black hole charge and masses as well as the black entropy, temperature, and electric potential have been calculated from the geometrical and thermodynamical approaches, separately. Through comparison of the results arisen from these two alternative approaches, the validity of the thermodynamical first law has been proved for both of the new black hole solutions in the Einstein frame. Making use of the canonical ensemble method, a black hole stability or phase transition analysis has been performed. Regarding the black hole heat capacity, with the black hole charge as a constant, the points of type-1 and type-2 phase transitions have been determined. Also, the ranges of the black hole horizon radius at which the Einstein black holes are thermally stable have been obtained for both of the new black hole solutions. Then making use of the inverse transformation relations, two new classes of the string black hole solutions have been obtained from their Einstein counterpart. The thermodynamics and thermal stability of the new string black hole solutions have been investigated. It has been found that thermodynamic properties of the new charged black holes are identical in the Einstein and Jordan frames.

DC conductivity with external magnetic field in hyperscaling violating geometry

We investigate the holographic DC conductivity of (2[Formula: see text]+[Formula: see text]1)-dimensional systems while considering hyperscaling violating geometry in bulk. We consider Einstein–Maxwell-dilaton system with two gauge fields and Liouville-type potential for dilaton. We also consider axionic fields in bulk to introduce momentum relaxation in the system. We apply an external magnetic field to study the response of the system and obtain analytic expressions for DC conductivity, Hall angle and (thermo)electric conductivity.

Thermodynamics of charged dilatonic BTZ black holes in rainbow gravity

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.

Nonlinearly charged black holes in the scalar-tensor modified gravity theory

Starting from the action of the scalar-tensor modified gravity theory coupled to the power law nonlinear electrodynamics and making use of the suitable transformation relations, the corresponding action of the Einstein-power-Maxwell-dilaton gravity theory has been obtained. Thermodynamical properties of the new charged dilatonic black holes have been investigated in the presence of a power Maxwell field as the nonlinear electrodynamics. Making use of a special form of a scalar field, it has been found that the scalar potential can be written as the linear combination of three Liouville-type potentials. Three new classes of spherically symmetric charged dilatonic black hole solutions have been obtained as the exact solutions to the field equations of the Einstein-power-Maxwell-dilaton theory. The conserved and thermodynamical quantities, related to the new black hole solutions, have been calculated from geometrical and thermodynamical approaches separately. Through comparison of the results obtained from these two alternative approaches, the validity of the first law of black hole thermodynamics has been confirmed for either of three new black hole solutions. Thermal stability or phase transition of the new black hole solutions has been analyzed, making use of the canonical ensemble method, and by calculating the black hole heat capacity at the fixed black hole charge. The points of type one and type two phase transitions as well as the ranges at which the black holes are locally stable have been determined precisely. The nonlinearly charged string black hole solutions have been obtained from their Einstein's counterparts. The thermodynamical properties as well as the thermal stability of the new charged string black holes have been investigated by utilizing the canonical ensemble method.

Dilatonic black holes in gravity\u2019s rainbow with a nonlinear source: the effects of thermal fluctuations

This paper is devoted to an investigation of nonlinearly charged dilatonic black holes in the context of gravity’s rainbow with two cases: (1) by considering the usual entropy, (2) in the presence of first order logarithmic correction of the entropy. First, exact black hole solutions of dilatonic Born–Infeld gravity with an energy dependent Liouville-type potential are obtained. Then, thermodynamic properties of the mentioned cases are studied, separately. It will be shown that although mass, entropy and the heat capacity are modified due to the presence of a first order correction, the temperature remains independent of it. Furthermore, it will be shown that divergences of the heat capacity, hence phase transition points are also independent of a first order correction, whereas the stability conditions are highly sensitive to variation of the correction parameter. Except for the effects of a first order correction, we will also present a limit on the values of the dilatonic parameter and show that it is possible to recognize AdS and dS thermodynamical behaviors for two specific branches of the dilatonic parameter. In addition, the effects of nonlinear electromagnetic field and energy functions on the thermodynamical behavior of the solutions will be highlighted and dependency of critical behavior, on these generalizations will be investigated.

Thermodynamics of ( 2+1 )-dimensional black holes in Einstein-Maxwell-dilaton gravity

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.

Thermodynamics of novel charged dilatonic BTZ black holes

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.

Thermodynamics of rotating black branes in higher dimensional Einstein – nonlinear electrodynamics – dilaton gravity

In this paper, we propose a n-dimensional action in which gravity is coupled to exponential nonlinear electrodynamics and scalar dilaton field with Liouville-type potential. By varying the action, we obtain the field equations. Then, we construct a new class of charged, rotating black brane solutions, with k = [(n – 1)/2] rotation parameters, of this theory. Because of the presence of the Liouville-type dilaton potential, the asymptotic behavior of the obtained solutions is neither flat nor (anti)-de Sitter. We investigate the causal structure of the space–time in ample details. We find the suitable counter term that removes the divergences of the action in the presence of the dilaton field, and calculate the conserved and thermodynamic quantities of the space–time. Interestingly enough, we find that the conserved quantities crucially depend on the dilaton coupling constant, α, while they are independent of the nonlinear parameter, β. We also check the validity of the first law of thermodynamics on the black brane horizon. Finally, we study thermal stability of the solutions by computing the heat capacity in the canonical ensemble. We disclose the effects of rotation parameter, nonlinearity of electrodynamics, and dilaton field on the thermal stability conditions.