Power-Maxwell Electrodynamics Research Articles

Spontaneous scalarization in Einstein-power-Maxwell-scalar models

We study the spontaneous scalarization of charged black holes in Einstein’s gravity minimally coupled to power-Maxwell electrodynamics which, in turn, is non-minimally coupled to a real scalar field. We point out the existence of a specific power for which the scalarized solution is well-behaved, and entropically preferred in comparison to the scalar-free charged black hole solution.

Charged particles in the background of the Kiselev solution in power-Maxwell electrodynamics

Charged particles in the background of the Kiselev solution in power-Maxwell electrodynamics

Thermodynamics of higher-dimensional Brans-Dicke black holes in the presence of a conformal-invariant field inspired by power-Maxwell electrodynamics

Abstract By use of the conformal transformations, in addition to translating the Brans-Dicke (BD) action to the Einstein frame (EF), we introduce an electromagnetic Lagrangian which preserves conformal invariance. We solve the EF field equations, which mathematically are confronted with the problem of indeterminacy, by use of an exponential ansatz function. When the self-interacting potential is absent or is taken constant in the BD action, the exact solution of this theory is just that of Einstein-conformal-invariant theory with a trivial scalar field. This is higher-dimensional (HD) analogues of the same considered in [1]. The EF general solution admits two classes of black holes (BHs) with non-flat and non-AdS asymptotic behavior which can produce extreme and multi-horizon ones. We obtain the exact solutions of BD-conformal-invariant theory, by applying inverse conformal transformations, which show two classes of extreme and multi-horizon BHs too. Based on the fact that thermodynamic quantities remain unchanged under conformal transformations, we show that the first law of BH thermodynamics is valid in the Jordan frame (JF). We analyze thermal stability of the HD BD-conformal-invariant BHs by use of the canonical ensemble method.

Holographic entanglement entropy with Power-Maxwell electrodynamics in higher dimensional AdS black hole spacetime* *Supported by the National Natural Science Foundation of China (11665015), the Guizhou Provincial Science and Technology Planning Project of China (qiankehejichu-ZK[2021]yiban026), and the Guizhou Province ordinary institutions of higher learning top science and technology talents Support plan of China (qianjiaoheKY[2019]062).

We investigate the behaviors of the scalar operator and holographic entanglement entropy in the metal/superconductor phase transition with Power-Maxwell electrodynamics in a higher dimensional background away from the probe limit. We observe that the larger parameters b and q make the condensation of the scalar operator more difficult, and the critical temperature decreases more slowly as the factors increase. In the belt geometry, the value of the entanglement entropy in the metal and superconductor phases is not only related to the the strength of the Power-Maxwell field but also to the width of the strip geometry. At the phase transition point, the discontinuous slope of entanglement entropy is universal for different model factors. It turns out that holographic entanglement entropy is a powerful tool to probe the properties of the phase transition in this holographic superconductor model.

Kiselev solution in power-Maxwell electrodynamics

In this work we reconsider the solution describing black holes surrounded by a quintessencelike fluid. This geometry was introduced by Kiselev in 2003 and its physical source was originally modeled by an anisotropic fluid. We show that the Kiselev geometry is actually an exact solution of the Einstein equations coupled to nonlinear electrodynamics. More specifically, we show that the Kiselev geometry becomes an exact solution in the context of power-Maxwell electrodynamics, using either an electric ansatz or a magnetic one. In both cases the physical source can be modeled by a power-Maxwell Lagrangian, albeit with different powers corresponding to the electric or the magnetic charges. We briefly investigate the motion of charged particles in this geometry. Finally, we give the proper interpretation of the black-hole thermodynamics in this context. Similarly to the Schwarzschild-de Sitter case, we note the presence of the Schottky peaks in the heat capacity, signaling out the possibility of this thermodynamic black hole system to function as a continuous heat machine.

Meissner-like effect and conductivity of power-Maxwell holographic superconductors

The full description of a superconductor requires that it has an infinite DC conductivity (or zero electrical resistivity) as well as expels the external magnetic fields. Thus, for any holographic superconductor which is dual to a real superconductor, it is necessary to examine, simultaneously, these two features based on the gauge/gravity duality. In this paper, we explore numerically these two aspects of the higher dimensional holographic superconductors, in the presence of a Power-Maxwell electrodynamics as the gauge field. At first, we calculate the critical temperature, condensation, conductivity, and superconducting gap, in the absence of magnetic field and disclose the effects of both power parameter, $s$, as well as the spacetime dimensions, $d$, on this quantities. Then, we immerse the superconductor into an external magnetic field, $B$, and observe that with increasing the magnetic field, the starting point of condensation occurs at temperature less than the critical temperature, $T_{c}$, in the absence of magnetic field. This implies that at a fixed temperature, we can define a critical magnetic field, above which the critical temperature goes to zero which is similar to the Meissner effect in superconductor. In these indications, we also try to show the distinction of the conformal invariance of the Power-Maxwell Lagrangian that occurs for $s=d/4$.

Three-dimensional scalar-tensor black holes with conformally invariant electrodynamics

We explore three-dimensional scalar-tensor black hole solutions in the presence of power-Maxwell electrodynamics. By applying the conformal transformations on the action of scalar-tensor theory, we show that the electromagnetic Lagrangian remains invariant for a specific amount of power. In addition, the gravitational action transforms to that of Einstein-dilaton gravity theory. Through solving the field equations of this theory, we obtain two novel classes of Einstein-dilaton black hole solutions. Next, proceed to investigate the thermodynamic properties of the solutions and show that thermodynamical first law is valid for both of our solutions. Then, we analyze the thermal stability or phase transition of the black holes based on the canonical ensemble method. Finally, we obtain the Jordan frame scalar-tensor black hole solutions, by imposing the inverse conformal transformations, from their Einstein-dilaton counterparts and investigate their thermodynamics and thermal stability properties.

Noncommutative effects on holographic superconductors with power Maxwell electrodynamics

The matching method is employed to analytically investigate the properties of holographic superconductors in higher dimensions in the framework of power Maxwell electrodynamics taking into account the effects of spacetime noncommutativity. The relationship between the critical temperature and the charge density and the value of the condensation operator is obtained first. The Meissner like effect is then studied. The analysis indicates that larger values of the noncommutative parameter and the parameter q appearing in the power Maxwell theory make the condensate difficult to form. The critical magnetic field however increases with increase in the noncommutative parameter θ.

Holographic conductivity in the massive gravity with power-law Maxwell field

We obtain a new class of topological black hole solutions in (n+1)-dimensional massive gravity in the presence of the power-Maxwell electrodynamics. We calculate the conserved and thermodynamic quantities of the system and show that the first law of thermodynamics is satisfied on the horizon. Then, we investigate the holographic conductivity for the four and five dimensional black brane solutions. For completeness, we study the holographic conductivity for both massless (m=0) and massive (m≠0) gravities with power-Maxwell field. The massless gravity enjoys translational symmetry whereas the massive gravity violates it. For massless gravity, we observe that the real part of conductivity, Re[σ], decreases as charge q increases when frequency ω tends to zero, while the imaginary part of conductivity, Im[σ], diverges as ω→0. For the massive gravity, we find that Im[σ] is zero at ω=0 and becomes larger as q increases (temperature decreases), which is in contrast to the massless gravity. It also has a maximum value for ω≠0 which increases with increasing q (with fixed p) or increasing p (with fixed q) for (2+1)-dimensional dual system, where p is the power parameter of the power-law Maxwell field. Interestingly, we observe that in contrast to the massless case, Re[σ] has a maximum value at ω=0 (known as the Drude peak) for p=(n+1)/4 (conformally invariant electrodynamics) and this maximum increases with increasing q. In this case (m≠0) and for different values of p, the real and imaginary parts of the conductivity has a relative extremum for ω≠0. Finally, we show that for high frequencies, the real part of the holographic conductivity have the power law behavior in terms of frequency, ωa where a∝(n+1−4p). Some similar behaviors for high frequencies in possible dual CFT systems have been reported in experimental observations.

Effects of backreaction on power-Maxwell holographic superconductors in Gauss–Bonnet gravity

We analytically and numerically investigate the properties of s-wave holographic superconductors by considering the effects of scalar and gauge fields on the background geometry in five dimensional Einstein-Gauss-Bonnet gravity. We assume the gauge field to be in the form of the Power-Maxwell nonlinear electrodynamics. We employ the Sturm-Liouville eigenvalue problem for analytical calculation of the critical temperature and the shooting method for the numerical investigation. Our numerical and analytical results indicate that higher curvature corrections affect condensation of the holographic superconductors with backreaction. We observe that the backreaction can decrease the critical temperature of the holographic superconductors, while the Power-Maxwell electrodynamics and Gauss-Bonnet coefficient term may increase the critical temperature of the holographic superconductors. We find that the critical exponent has the mean-field value $\beta=1/2$, regardless of the values of Gauss-Bonnet coefficient, backreaction and Power-Maxwell parameters.

The upper critical magnetic field of holographic superconductor with conformally invariant Power–Maxwell electrodynamics

The properties of (d–1)-dimensional s-wave holographic superconductor in the presence of Power–Maxwell field is explored. We study the probe limit in which the scalar and gauge fields do not backreact on the background geometry. Our study is based on the matching of solutions on the boundary and on the horizon at some intermediate point. At first, the case without external magnetic field is considered, and the critical temperature is obtained in terms of the charge density, the dimensionality, and the Power–Maxwell exponent. Then, a magnetic field is turned on in the d-dimensional bulk, which can influence the (d–1)-dimensional holographic superconductor at the boundary. The phase behavior of the corresponding holographic superconductor is obtained by computing the upper critical magnetic field in the presence of Power–Maxwell electrodynamics, characterized by the power exponent q. Interestingly, it is observed that in the presence of a magnetic field, the physically acceptable phase behavior of the holographic superconductor is obtained for q = d/4, which guaranties the conformal invariance of the Power–Maxwell Lagrangian. The case of physical interest in five space–time dimensions (d = 5, and q = 5/4) is considered in detail, and compared with the results obtained for the usual Maxwell electrodynamics q = 1 in the same dimensions.

Analytical and numerical study of Gauss-Bonnet holographic superconductors with Power-Maxwell field

We provide an analytical as well as a numerical study of the holographic $s$-wave superconductors in Gauss-Bonnet gravity with Power-Maxwell electrodynamics. We limit our study to the case where scalar and gauge fields do not have an effect on the background metric. We use a variational method, based on Sturm-Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. Interestingly enough, we observe that unlike Born-Infeld-like nonlinear electrodynamics which decrease the critical temperature compared to the linear Maxwell field, the Power-Maxwell electrodynamics is able to increase the critical temperature of the holographic superconductors in the sublinear regime. We find that requiring the finite value for the gauge field on the asymptotic boundary $r\rightarrow \infty$, restricts the power parameter, $q$, of the Power-Maxwell field to be in the range $1/2<q<{(d-1)}/{2}$. Our study indicates that it is quite possible to make condensation \emph{easier} as $q$ \emph{decreases} in its allowed range. We also find that for all values of $q$, the condensation can be affected by the Gauss-Bonnet coefficient $\alpha$. However, the presence of the Gauss-Bonnet term makes the transition slightly harder. Finally, we obtain an analytic expression for the order parameter and thus obtain the associated critical exponent near the phase transition. We find that the critical exponent has its universal value of $\beta=1/2$ regardless of the parameters $q$, $\alpha$ as well as dimension $d$, consistent with mean-field values obtained in previous studies.

AdS/CFT superconductors with Power Maxwell electrodynamics: Reminiscent of the Meissner effect

Based on an analytic scheme and neglecting the back reaction effect several crucial properties of holographic s-wave superconductors have been investigated in the presence of an external magnetic field in the background of a D-dimensional Schwarzschild AdS space–time. Inspired by low energy limit of heterotic string theory, in the present Letter we replace the conventional Maxwell action by a Power Maxwell action. Immersing the holographic superconductors in an external static magnetic field the spatially dependent condensate solutions have been obtained analytically. Interestingly enough it is observed that condensation can form only below a certain critical field strength (Bc). Finally, and most importantly it is observed that the value of this critical field strength increases as the mass of the scalar particles gets higher, which indicates the onset of a harder condensation.