This paper investigates thermodynamics, quasi-normal modes, thermal fluctuations and phase transitions of Reissner-Nordström black hole with the effects of non-linear electrodynamics. We first compute the expressions for Hawking temperature, entropy and heat capacity of this black hole and then obtain a relation between Davies's point and quasi-normal modes with non-linear electrodynamics. We also observe the effects of logarithmic corrections on uncorrected thermodynamic quantities such as entropy, Hawking temperature, Helmholtz free energy, internal energy, Gibbs free energy, enthalpy and heat capacity. It is found that presence of non-linear electrodynamic parameter induces more instability in black holes of large radii. Finally, we analyze the phase transitions of Hawking temperature as well as heat capacity in terms of entropy for different values of charge ($q$), horizon radius ($r_{+}$) and coupling parameter ($α$). We obtain that Hawking temperature changes its phase from positive to negative for increasing values of $q$ and $r_{+}$ while it shows opposite trend for higher values of $α$. The heat capacity changes its phase from negative to positive for large values of charge, horizon radius and coupling parameter.
It is well known that the Smarr formula does not hold for black holes in non-linear electrodynamics. The main reason for this is the fact that the trace of the energy momentum tensor for nonlinear electrodynamics does not vanish as it is for Maxwell's electrodynamics. Starting from the Komar integral, we derived a new Smarr-type formula for spherically symmetric static electrically charged black hole solutions in nonlinear electrodynamics. We show that this general formula is in agreement with some that are obtained for black hole solutions with nonlinear electrodynamics.
Comment on "Regular magnetically charged black holes from nonlinear electrodynamics: Thermodynamics, light deflection, and orbital dynamics" by Aydiner, Sucu and Sakalli
We present a family of nonlinear electrodynamics models that are free of the infinite self-energy of the point charge. Each model is dependent on a dimensional nonlinearity parameter and is determined by the integer value of a dimensionless parameter n. The Born-Infeld model is recovered when n = 1. Some of the characteristics of this family are studied. In addition, we study the solutions of electrically charged AdS black holes, which result from coupling these electrodynamic models to General Relativity. A Smarr formula consistent with the first law of thermodynamics is also obtained in an e…
The near horizon limit of the extreme nonlinear black hole is investigated. It is shown that resulting geometry belongs to the AdS2xS2 class with different modules of curvatures of subspaces and could be described in terms of the Lambert functions. It is demonstrated that the considered class of Lagrangians does not admit solutions of the Bertotti-Robinson type.
Motivated by the string corrections on the gravity and electrodynamics sides, we consider a quadratic Maxwell invariant term as a correction of the Maxwell Lagrangian to obtain exact solutions of higher dimensional topological black holes in Gauss-Bonnet gravity. We first investigate the asymptotically flat solutions and obtain conserved and thermodynamic quantities which satisfy the first law of thermodynamics. We also analyze thermodynamic stability of the solutions by calculating the heat capacity and the Hessian matrix. Then, we focus on horizon-flat solutions with adS asymptote and produc…
We obtain a magnetically charged regular black hole in general relativity. The source to the Einstein field equations is nonlinear electrodynamic field in a physically reasonable model of nonlinear electrodynamics (NED). "Physically" here means the NED model is constructed on the basis of three conditions: the Maxwell asymptotic in the weak electromagnetic field limit; the presence of vacuum birefringence phenomenon; and satisfying the weak energy condition (WEC). In addition, we analyze the thermodynamic properties of the regular black hole in two ways. According to the usual black hole therm…
In this paper, we study the thermodynamical properties of the (2+1)dimensional black hole with a non-linear electrodynamics and without cosmological constant using the Generalized Uncertainty Principle (GUP). This approach shows that there is a maximum temperature for the black hole depending only on the electric charge and corresponding to the minimum radius of the event horizon, of the order of the Planck scale. Finally we show that the heat capacity for this black hole has the expected behavior.
In this paper we have studied electrically charged black holes in a new model of nonlinear electrodynamics introduced by Kruglov in Ref. [1]. There are two parameters for the theory and the black hole could have up to two horizons. Thermodynamics is studied in the extended phase space where the pressure is proportional to the cosmological constant. First law and the Smarr formula are derived. There are phase transitions similar to the Van der Waals liquid-gas phase transitions. Black hole is also studied as a heat engine and have discussed how the parameters in the nonlinear electrodynamics th…
This paper deals with the problem of a point-like charged source under the influence of the external electromagnetic field in terms of perturbation theory for GR equations. It is obtained that GR, in contrast with the classical electrodynamics, in linear perturbation theory predicts an unlimited growth of the dipole perturbation. It is shown that the reason for this unlimited perturbation growth might be related to the presence of the unstable rotational perturbation mode. The analysis of the conditions under which this instability may disappear is performed. The momentum value at which the st…
Nonlinear electrodynamic (NLED) theories are well-motivated for their extensions to classical electrodynamics in the strong field regime, and have been extensively investigated in seeking for regular black hole solutions. In this paper, we focus on two spherically symmetric and static black hole solutions based on two types of NLED models: the Euler-Heisenberg NLED model and the Bronnikov NLED model, and calculate the weak deflection angle of light by these two black holes with the help of the Gauss-Bonnet theorem. We investigate the effects of the one-loop corrections to quantum electrodynami…
In this work, we have considered the magnetic universe in non-linear electrodynamics. The Einstein's field equations for non-flat FRW model have been considered when the universe is filled with the matter and magnetic field only. We have discussed the validity of the generalized second law of thermodynamics of the magntic universe bounded by Hubble, apparent, particle and event horizons using Gibb's law and the first law of thermodynamics for interacting and non-interacting scenarios. It has been shown that the GSL is always satisfied for Hubble, apparent and particle horizons but for event ho…
The time-like naked singularities of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov is investigated within the framework of quantum mechanics. In view of quantum mechanics, the space-time is quantum regular provided that the time evolution of the test quantum wave packet uniquely propagates on an underlying background. Rigorous calculations have shown that when the singularity is probed with specific quantum wave/particle modes, the quantum wave operator turns out to be essentially self-adjoint. Thus, the time…
Along the last decades, several regular black hole (BH) solutions, i.e., singularity-free BHs, have been proposed and associated to nonlinear electrodynamics models minimally coupled to general relativity. Within this context, it is of interest to study how those nonlinear-electrodynamic-based regular BHs (RBHs) would interact with their astrophysical environment. We investigate the propagation of a massless test scalar field in the background of an electrically charged RBH solution, obtained by Eloy Ayón-Beato and Alberto García. Using a numerical approach, we compute the absorption cross sec…
In this paper, we present the analytic solution for Anti-de Sitter-Nonlinear electrodynamics (AdS-NED) black hole in four dimensions. We study tunneling of vector particles from the AdS-NED black hole to find Hawking temperature as well as its thermodynamical properties in usual and extended phase space. Then we explore the properties of pressure-volume criticality by analyzing the phase diagram and its free energy. Finally, we investigate the Joule-Thomson coefficient, in which the inversion curve of warming and cooling are studied, and the ratio between the inverse temperature and critical t…
This paper aims to investigate the astrophysical applicability of the electrically and magnetically charged black hole solutions obtained in a model of nonlinear electrodynamics proposed by Kruglov (Ann. Phys. Berlin 2017, 529, 170073). Theoretical calculations of the bending angles and gravitational redshifts from the theory of general relativity are studied numerically by using the stellar data of charged compact objects and a hypothetical quark star model. Calculations have revealed that although the theoretical outcomes differ from the linear Maxwell case, the plotted bending angles coinci…
We summarize the main features of a class of \emph{asymptotically anomalous} (asymptotically flat, but non Schwarzschild-like) gravitational configurations in models of gravitating non-linear electrodynamics in three space dimensions, whose Lagrangian densities are defined as arbitrary functions of the two field invariants and constrained by several physical admissibility conditions. This class of models and their associated electrostatic spherically symmetric black hole solutions are characterized by the behaviours of the Lagrangian densities around the vacuum and at the boundary of their dom…
We study the propagation of charged scalar fields in the background of $2+1$-dimensional Coulomb-like AdS black holes, and we show that such propagation is unstable under Dirichlet boundary conditions. However, all the unstable modes are superradiant and all the stable modes are non-superradiant, according with the superradiant condition. Mainly, we show that when the scalar field is charged the quasinormal frecuencies (QNFs) are always complex, contrary to the uncharged case, where for small values of the black hole charge the complex QNFs are dominant, while that for bigger values of the bla…
We derive the equations for the odd and even parity perturbations of coupled electromagnetic and gravitational fields of a black hole with an electric charge within the context of general nonlinear electrodynamics. The Lagrangian density is a generic function of the Lorentz invariant scalar quantities of the electromagnetic fields. We include the Hodge dual of the electromagnetic field tensor and the cosmological constant in our calculations. For each type of parity, we reduce the system of Einstein field equations coupled to nonlinear electrodynamics to two coupled Schrödinger-type wave equat…
The "black-bounce" spacetime geometries, were recently proposed in [A. Simpson, M. Visser, JCAP 02 (2019) 042] as regular black holes that bouncing into a future incarnation of the universe. In this work we will present several black-bounce exact solutions of General Relativity. Among them is a novel type of black-bounce solutions, which in contrast of the Simpson-Visser type [A. Simpson, M. Visser, JCAP 02 (2019) 042], do not have the Ellis wormhole metric as a particular case. The source of these solutions are linear superposition of phantom scalar fields and nonlinear electromagnetic fields…
In this paper, we study the nonlinear electrodynamics in the framework of $f(T)$ gravity for FRW universe along with dust matter, magnetic and torsion contributions. We evaluate the equation of state and deceleration parameters to explore the accelerated expansion of the universe. The validity of generalized second law of thermodynamics for Hubble and event horizons is also investigated in this scenario. For this purpose, we assume pole-like and power-law forms of scale factor and construct $f(T)$ models. The graphical behavior of the cosmological parameters versus smaller values of redshift $…
This work examines the magnetized black holes of Lovelock gravity in the presence of double-logarithmic electrodynamics. In this context, the Lovelock polynomial is found and the accompanying thermodynamic quantities, such as mass, entropy, Hawking temperature, and heat capacity are determined. This new model of nonlinear electrodynamics is used to calculate the black hole solutions of Einstein, Gauss-Bonnet and third order Lovelock gravities as well. The impacts of the double-logarithmic electromagnetic field on the black hole thermodynamics in these particular theories are examined and the r…
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, e…
We investigate the scattering properties of a massless scalar field in the background of a charged Ayón-Beato-García regular black hole solution. Using a numerical approach, we compute the differential scattering cross section for arbitrary values of the scattering angle and of the incident wave frequency. We compare our results with those obtained via the classical geodesic scattering of massless particles, as well as with the semiclassical glory approximation, and show that they present an excellent agreement in the corresponding limits. We also show that Ayón-Beato-García and Reissner-Nords…
We address the question of existence of regular spherically symmetric electrically charged solutions in Nonlinear Electrodynamics coupled to General Relativity. Stress-energy tensor of the electromagnetic field has the algebraic structure $T_0^0=T_1^1$. In this case the Weak Energy Condition leads to the de Sitter asymptotic at approaching a regular center. In de Sitter center of an electrically charged NED structure, electric field, geometry and stress-energy tensor are regular without Maxwell limit which is replaced by de Sitter limit: energy density of a field is maximal and gives an effect…
We study quasinormal modes related to gravitational and electromagnetic perturbations of spherically symmetric charged black holes in nonlinear electrodynamics. Beyond the linear Maxwell electrodynamics, we consider a class of Lagrangian with higher-order corrections written by the electromagnetic field strength and its Hodge dual with arbitrary coefficients, and we parametrize the corrections for quasinormal frequencies in terms of the coefficients. It is confirmed that the isospectrality of quasinormal modes under parity is generally violated due to nonlinear electrodynamics. As applications…
We study a non-local ghost-free Lorentz invariant modification of the Maxwell equations in four- and higher-dimensional flat spacetimes. We construct solutions of these equations for stationary charged and magnetized objects and use them to find the field created by such objects moving with the speed of light.
Regarding the wide applications of dilaton gravity in the presence of electrodynamics, we introduce a suitable Lagrangian for the coupling of dilaton with gauge field. There are various Lagrangians which show the coupling between scalar fields and electrodynamics with correct special situations. In this paper, taking into account conformal transformation of Brans-Dicke theory with an electrodynamics Lagrangian, we show that how scalar field should couple with electrodynamics in dilaton gravity. In other words, in order to introduce a correct Lagrangian of dilaton gravity, one should check at l…
The \textit{axial} electromagnetic (EM) perturbations of the black hole (BH) solutions in general relativity coupled to nonlinear electrodynamics (NED) were studied for both electrically and magnetically charged BHs, assuming that the EM perturbations do not alter the spacetime geometry in our preceding paper [Phys. Rev. D 97, 084058 (2018)]. Here, as a continuation of that work, the formalism for the \textit{polar} EM perturbations of the BHs in general relativity coupled to the NED is presented. We show that the quasinormal modes (QNMs) spectra of polar EM perturbations of the electrically a…
After many years of efforts, the first nonlinearly charged rotating black hole has been finally reported by Garcia-Diaz in two recent works. This is an important result that was pending in General Relativity, since nonlinear generalizations of the Kerr-Newman solution were not yet known. Unfortunately, the Lagrangian supporting this configuration cannot be expressible in terms of the standard invariants using elementary functions. In the present work we circumvent this problem by using the formulations of nonlinear electrodynamics in terms of mixed electromagnetic eigenvalues, introduced by Sa…
We investigate $4D$ Einstein-Gauss-bonnet gravity coupled to exponential electrodynamics in AdS background and found a static, spherically symmetric exact black hole solution. The horizon structure of black hole is discussed. Treating the cosmological constant as pressure, we drive first law of black hole thermodynamics in extended phase space. We compute the electrostatic potential and vacuum polarization of the black hole. To study local thermodynamical stability specific heat of the black hole is computed. Finally, we study Helmholtz free energy to analyse the global stability of black hole…
In this paper, we obtain topological black hole solutions of third order Lovelock gravity couple with two classes of Born-Infeld type nonlinear electrodynamics with anti-de Sitter asymptotic structure. We investigate geometric and thermodynamics properties of the solutions and obtain conserved quantities of the black holes. We examine the first law of thermodynamics and find that the conserved and thermodynamic quantities of the black hole solutions satisfy the first law of thermodynamics. Finally, we calculate the heat capacity and determinant of Hessian matrix to evaluate thermal stability i…
On the basis of two requirements: the avoidance of the curvature singularity and the Maxwell theory as the weak field limit of the nonlinear electrodynamics, we find two restricted conditions on the metric function of $(2+1)$-dimensional regular black hole in general relativity coupled with nonlinear electrodynamics sources. By the use of the two conditions, we obtain a general approach to construct $(2+1)$-dimensional regular black holes. In this manner, we construct four $(2+1)$-dimensional regular black holes as examples. We also study the thermodynamic properties of the regular black holes…
We prove a no Cauchy horizon theorem for general nonlinear electrodynamics black holes with charged scalar hairs. By constructing a radially conserved charged, we show that there is no inner Cauchy horizon for both spherical and planar symmetric cases, independent of the form of scalar potential and nonlinear electrodynamics. After imposing the null energy condition, we are also able to rule out the existence of the Cauchy horizon for the hyperbolic black holes. We take the Born-Infeld black hole as a concrete example to study the interior dynamics beyond the event horizon. When the contributi…
In the present work we study the scale dependence at the level of the effective action of charged black holes in Einstein-Maxwell as well as in Einstein-power-Maxwell theories in (2+1)-dimensional spacetimes without a cosmological constant. We allow for scale dependence of the gravitational and electromagnetic couplings, and we solve the corresponding generalized field equations imposing the "null energy condition". Certain properties, such as horizon structure and thermodynamics, are discussed in detail.
We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve fa…
Super-entropic black holes possess finite-area but noncompact event horizons and violate the reverse isoperimetric inequality. It has been conjectured that such black holes always have negative specific heat at constant volume $C_{V}$ or negative specific heat at constant pressure $C_{P}$ whenever $C_{V}>0$, making them unstable in extended thermodynamics. In this paper, we test this instability conjecture on a family of nonlinear electrodynamics black holes, namely $3$D Einstein-Born-Infeld (EBI) AdS black holes. Our results show that when nonlinear electrodynamics effects are weak, the insta…
In this paper we will show that using the cosmological constant as a new thermodynamical state variable, the differential and integral mass formulas of the first law of thermodynamics for asymptotic flat spacetimes can be extended to (2+1) dimensional charged BTZ black holes and charged de Sitter space.
In nonlinear electrodynamics coupled to gravity, regular spherically symmetric electrically charged solutions satisfy the weak energy condition and have obligatory de Sitter centre. By the Gürses-Gürsey algorithm they are transformed to spinning electrically charged solutions asymptotically Kerr-Newman for a distant observer. Rotation transforms de Sitter center into de Sitter vacuum surface which contains equatorial disk $r=0$ as a bridge. We present general analysis of the horizons, ergoregions and de Sitter surfaces, as well as the conditions of the existence of regular solutions to the fie…
In this work we study thermodynamics of 2+1-dimensional static black holes with a nonlinear electric field. Besides employing the standard thermodynamic approach, we investigate the black hole thermodynamics by studying its thermodynamic geometry. We compute the Weinhold and Ruppeiner metrics and compare the thermodynamic geometry with the standard description on the black hole thermodynamics. We further consider the cosmological constant as an additional extensive thermodynamic variable. In the thermodynamic equilibrium three dimensional space, we compute the efficiency of the heat engine and…
Thermodynamics and phase transitions of charged-AdS black holes in dRGT massive gravity with nonlinear electrodynamics
Centre for Theoretical Physics, Jamia Millia Islamia（贾米亚米利亚伊斯兰大学理论物理中心）；Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江工业大学理论与宇宙学研究所）；Phenikaa Institute for Advanced Study, Phenikaa University（菲尼亚卡大学高级研究院）；Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal（夸祖鲁-纳塔尔大学数学、统计与计算机科学学院天体物理与宇宙学研究单元）
New five-dimensional charged AdS black hole solutions are found in Einstein-Gauss-Bonnet gravity and the nonlinear electrodynamics. These solutions include regular black holes as well as extremal black holes. The first law of the black hole thermodynamics is confirmed in the extended phase space where the cosmological constant is treated as the pressure. The first and second order phase transitions are investigated by observing the behavior of the heat capacity at constant pressure and the Gibbs free energy. In addition, the equation of state for the black holes and their $P-V$ criticality are…
We construct an exact black hole solution for the Einstein gravity coupled with the nonlinear electrodynamics (which corresponds to the Maxwell electrodynamics in the weak field limit) in the presence of a cloud of strings as the source. We study the thermodynamical properties of the black hole solutions and derive the corrected first-law of thermodynamics. The presence of a cloud of strings does not affect the stability of the present black hole. However, a second-order phase transition exists for this system at a critical horizon radius. Furthermore, we study the quasinormal modes and their …
The Bronnikov model of nonlinear electrodynamics is investigated in general relativity. The magnetic black hole is considered and we obtain a solution giving corrections to the Reissner-Nordström solution. In this model spacetime at $r\rightarrow\infty$ becomes Minkowski's spacetime. We calculate the magnetic mass of the black hole and the metric function. At some parameters of the model there can be one, two or no horizons. The Hawking temperature and the heat capacity of black holes are calculated. We show that a second-order phase transition takes place and black holes are thermodynamically…
We find non-commutative inspired electrically and magnetically charged black hole solutions in Euler-Heisenberg non-linear electrodynamics. For these solutions, we determine the non-commutative corrections to the horizon radius for the general and extremal case. We also analyse the weak, dominant and strong energy conditions and the shadow associated with these metrics.
The no-scalar-hair conjecture rules out the existence of asymptotically flat black holes with a scalar dressing for a large class of theories. No-scalar-hair theorems have been proved for the cases of neutral black holes and for charged black holes in the Maxwell electrodynamics. These theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Euler-Heisenberg type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. In comparison to the correspondi…
The non-existence of asymptotically flat, neutral black holes and asymptotically flat, charged black holes in the Maxwell electrodynamics, with non-trivial scalar field has been proved for a large class of scalar-tensor theories. The no-scalar-hair theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Born-Infeld type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. The causal structure and properties of the solutions are studied, and a com…
In this paper, I investigate the nonlinear magnetized black holes of massive gravity's rainbow. In order to achieve this, I use the double-logarithmic electromagnetic field as a matter source and derive the new anti-de Sitter black hole solution. The effects of the massive graviton, rainbow functions, and nonlinearity of the electromagnetic field on the black hole's inner and outer horizons are also studied. The black hole's thermodynamic properties are studied, and the mathematical expressions for temperature, heat capacity, and Gibbs free energy are found. The extended first law and Smarr's …
