Charged Black Hole Solutions Research Articles

Rotating and non-rotating AdS black holes in f(mathcal{T}) gravity non-linear electrodynamics

We derive new exact charged d-dimensional black hole solutions for quadratic teleparallel equivalent gravity, f(mathcal{T})=a_0+a_1mathcal{T}+a_2mathcal{T}^2, where mathcal T is the torsion scalar, in the case of non-linear electrodynamics. We give a specific form of electromagnetic function and find out the form of the unknown functions that characterize the vielbeins in presence of the electromagnetic field. It is possible to show that the black holes behave asymptotically as AdS solutions and contain, in addition to the monopole and quadrupole terms, other higher order terms whose source is the non-linear electrodynamics field. We calculate the electromagnetic Maxwell field and show that our d-dimensional black hole solutions coincide with the previous obtained one (Awad et al. in J High Energy Phys 13:1706.01773, 2017). The structure of the solutions show that there is a central singularity that is much mild in comparison with the respective one in general relativity. Finally, the thermodynamical properties of the solutions are investigated by calculating the entropy, the Hawking temperature, the heat capacity, and other physical quantities. The most important result of thermodynamics is that the entropy is not proportional to the area of the black hole. This inanition points out that we must have a constrain on the quadrupole term to get a positive entropy otherwise we get a negative value.

Particle motion around generic black holes coupled to non-linear electrodynamics

We study spherically symmetric magnetically charged generic black hole solutions of general relativity coupled to non-linear electrodynamics (NED). For characteristic values of the generic spacetime parameters we give the position of horizons in dependence on the charge parameter, demonstrating separation of the black hole and no-horizon solutions, and possibility of existence of solutions containing three horizons. We show that null, weak and strong energy conditions are violated when the outer horizon is approaching the center. We study effective potentials for photons and massive test particles and location of circular photon orbits (CPO) and innermost stable circular orbit (ISCO). We show that the unstable photon orbit can become stable, leading to the possibility of photon capture which affects on silhouette of the central object. The position of ISCO approaches the horizon with increasing charge parameter q and the energy at ISCO decreases with increasing charge parameter. We investigate this phenomenon and summarize for a variety of the generic spacetime parameters the upper estimate on the spin parameter of the Kerr black which can be mimicked by the generic charged black hole solutions.

Charged AdS black holes in Gauss\u2013Bonnet gravity and nonlinear electrodynamics

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 studied. Finally, the critical exponents are found to be the same as those of the Van der Waals fluid.

More on complexity in finite cut off geometry

It has been recently proposed that late time behavior of holographic complexity in a uncharged black brane solution of Einstein-Hilbert theory with boundary cut off is consistent with Lloyd's bound if we have a cut off behind the horizon. Interestingly, the value of this new cut off is fixed by the boundary cut off. In this paper, we extend this analysis to the charged black holes. Concretely, we find the value of this new cut off for charged small black hole solutions of Einstein-Hilbert-Maxwell theory, in which the proposed bound on the complexification is saturated. We also explore this new cut off in Gauss-Bonnet-Maxwell theory.

Dilaton black holes with power law electrodynamics

In this article, the new black hole solutions to the Einstein-power-Maxwell-dilaton gravity theory have been investigated in a four-dimensional space-time. The coupled scalar, electromagnetic and gravitational field equations have been solved in a static and spherically symmetric geometry. It has been shown that dilatonic potential, as the solution to the scalar field equation, can be written in the form of a generalized Liouville potential. Also, three classes of novel charged dilaton black hole solutions, in the presence of power law nonlinear electrodynamics, have been constructed out which are asymptotically non-flat and non-AdS. The conserved and thermodynamic quantities have been calculated from geometrical and thermodynamical approaches, separately. Since the results of these two alternative approaches are identical one can argue that the first law of black hole thermodynamics is valid for all of the new black hole solutions. The thermodynamic stability or phase transition of the black holes have been studied, 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 black holes are stable have been indicated by considering the heat capacity of the new black hole solutions. The global stability of the black holes have been studied through the grand canonical ensemble method. Regarding the Gibbs free energy of the black holes, the points of Hawking-Page phase transition and ranges of the horizon radii at which the black holes are globally stable have been determined.

Charged dilaton solutions and black hole formation in three dimensions

In this paper, we present the charged dilaton solutions and black hole formation in three dimensions. Firstly we revisit the famous Chan–Mann charged dilaton black hole, describing one parameter family of static charged black hole solution in three dimensional Einstein–Maxwell–Dilaton gravity. This solution with a special parameter choice b=4a can lead to the three dimensional string solution. Then we give another class of charged dilaton black hole solution with bne 4a. We discuss their geometrical properties, the horizon structure and the causal structure. The time-dependent solution is also presented, which can characterize the three dimensional charged black hole formation in Einstein–Dilaton gravity. Especially, there is no exact time-dependent solution describing the gravitational collapse to the Chan–Mann charged dilaton black hole. Finally, we discuss the gravitational collapse of a dilaton field in the context of the Cosmic Censorship Conjecture.

Thermodynamics of nonlinear electrodynamics black holes and the validity of weak cosmic censorship at charged particle absorption

We first use the Hamilton–Jacobi method to describe the motion in curved spacetime of a scalar particle and a fermion, which are shown to satisfy the same Hamilton–Jacobi equation. To investigate the laws of thermodynamics and the weak cosmic censorship, we focus on D-dimensional asymptotically AdS charged black hole solutions in general nonlinear electrodynamics (NLED). With absorbing a charged particle, the variation of the generic charged NLED black hole is calculated in the normal and extended phase spaces. In the normal phase space, where the cosmological constant and dimensionful parameters in NLED are fixed, the first and second laws of thermodynamics are satisfied. In the extended phase space, where the cosmological constant and dimensionful parameters in NLED are treated as thermodynamic variables, the first law of thermodynamics is also satisfied. However, the black hole entropy can either increase or decrease depending on the changes in the dimensionful parameters. Furthermore, we find that the weak cosmic censorship conjecture is valid for the extremal and near-extremal black holes in the both phase spaces.

Accretion onto Charged Black Holes in Einstein and Massive Theories of Gravity* *Supported by the Higher Education Commission (HEC) under Grant No. 9290/Balochistan/NRPU/R&D/HEC/2017

The accretion process is being investigated onto some important black holes such as Born-Infeld-AdS black hole, non-linear charged black hole solution in AdS space-time and Einstein-Yang-Mills massive gravity in the presence of Born-Infeld nonlinear electrodynamics. We find out the relations of radial velocity, energy density and change of mass for mention black holes and analyze their behavior graphically for different values of equation of state parameters ω. We also examine the relations for critical speed for these black holes. It is observed that for different state parameters different fluids exhibit different evolutions in black holes backgrounds. The energy density of some fluids is negative or positive near the black hole while other fluids become cause to increase or decrease in black hole mass.

Structure and thermodynamics of charged nonrotating black holes in higher dimensions

We analyze the structural and thermodynamic properties of $D$-dimensional ($D \geq 4$), asymptotically flat or Anti-de-Sitter, electrically charged black hole solutions, resulting from the minimal coupling of general nonlinear electrodynamics to General Relativity. This analysis deals with static spherically symmetric (elementary) configurations with spherical horizons. Our methods are based on the study of the behaviour (in vacuum and on the boundary of their domain of definition) of the Lagrangian density functions characterizing the nonlinear electrodynamic models in flat spacetime. These functions are constrained by some admissibility conditions endorsing the physical consistency of the corresponding theories, which are classified in several families, some of them supporting elementary solutions in flat space which are non topological solitons. This classification induces a similar one for the elementary black hole solutions of the associated gravitating nonlinear electrodynamics, whose geometrical structures are thoroughly explored. A consistent thermodynamic analysis can be developed for the subclass of families whose associated black hole solutions behave asymptotically as the Schwarzschild metric (in absence of a cosmological term). In these cases we obtain the behaviour of the main thermodynamic functions, as well as important finite relations among them. In particular, we find the general equation determining the set of extreme black holes for every model, and a general Smarr formula, valid for the set of elementary black hole solutions of such models. We also consider the one-parameter group of scale transformations, which are symmetries of the field equations of any nonlinear electrodynamics in flat spacetime.

Spontaneous scalarization of charged black holes at the approach to extremality

We study static, spherically symmetric and electrically charged black hole solutions in a quadratic Einstein-scalar-Gauss-Bonnet gravity model. Very similar to the uncharged case, black holes undergo spontaneous scalarization for sufficiently large scalar-tensor coupling γ – a phenomenon attributed to a tachyonic instability of the scalar field system. While in the uncharged case, this effect is only possible for positive values of γ, we show that for sufficiently large values of the electric charge Q two independent domains of existence in the γ-Q-plane appear: one for positive γ and one for negative γ. We demonstrate that this new domain for negative γ exists because of the fact that the near-horizon geometry of a nearly extremally charged black hole is AdS2×S2. This new domain appears for electric charges larger than approximately 74% of the extremal charge. For positive γ we observe that a singularity with diverging curvature invariants forms outside the horizon when approaching extremality.

Asymptotic magnetically charged non-singular black hole and its thermodynamics

Some very interesting solutions of the field equations of Einstein's general theory of relativity have been constructed in the framework of nonlinear electrodynamics. In particular, magnetically charged black hole solutions in the framework of exponential nonlinear electrodynamics have been obtained in general relativity in Kruglov (2017) [13]. Using this approach a magnetically charged non-singular black hole spacetime in the framework of exponential electrodynamics in some modified theory of gravity has been constructed in this letter. The metric describing asymptotic non-singular magnetized black hole is worked out in terms of the parameter of our model. When this parameter vanishes our solution reduces to the above mentioned black hole solution. Thermodynamics of the resulting solution is also discussed by calculating the Hawking temperature and heat capacity when the magnetic charge is constant. We also find out the point where the first order phase transition induced by temperature changes takes place. The quantum radiations from this black hole are also discussed and the mathematical expression for the rate of energy flux of these radiations has been obtained.

Rotating hairy black holes in AdS5 \xd7 S5

We present a numerical study of fully non-linear, rotating and charged hairy black hole solutions in five-dimensional anti-de Sitter space, which originate from a consistent truncation of mathcal{N}=8 supergravity, and can be consistently embedded in type IIB supergravity with AdS5×S5 asymptotics. The hairy black holes have one scalar field charged under a U(1) gauge field, and branch from the near-extremal Cvetič, Lü and Pope solutions. We give numerical evidence that the hairy solutions exist arbitrarily close to the BPS bound for all charges, and saturate it in the T → 0 and T → ∞ limits. We give further evidence for the conjecture of Markevičiūtė and Santos, that on the BPS bound, the rotating hairy black holes form a two-parameter family of solutions with finite entropy, and can be regarded as a one-parameter extension of the supersymmetric Gutowski and Reall black hole. We analyse the approach to the supersymmetric limit and explore the full phase diagram. In the planar horizon limit we find a two parameter family of rotating hairy black brane solutions which cannot be obtained via a Lorentz boost. The field theory dual exhibits a spontaneously generated current. The results of this paper suggest rich and intricate structure of hairy black hole solutions in AdS5×S5, and highlight their importance in understanding the thermodynamics of mathcal{N}=4 SYM.

Charged Einstein-æther black holes in n-dimensional spacetime

In this work, we investigate the [Formula: see text]-dimensional charged static black hole solutions in the Einstein-æther theory. By taking the metric parameter [Formula: see text] to be [Formula: see text], and [Formula: see text], we obtain the spherical, planar, and hyperbolic spacetimes, respectively. Three choices of the cosmological constant, [Formula: see text], [Formula: see text] and [Formula: see text], are investigated, which correspond to asymptotically de Sitter, flat and anti-de Sitter spacetimes. The obtained results show the existence of the universal horizon in higher dimensional cases which may trap any particle with arbitrarily large velocity. We analyze the horizon and the surface gravity of four- and five-dimensional black holes, and the relations between the above quantities and the electrical charge. It is shown that when the aether coefficient [Formula: see text] or the charge [Formula: see text] increases, the outer Killing horizon shrinks and approaches the universal horizon. Furthermore, the surface gravity decreases and approaches zero in the limit [Formula: see text] or [Formula: see text], where [Formula: see text] is the extreme charge. The main features of the horizon and surface gravity are found to be similar to those in [Formula: see text] case, but subtle differences are also observed.

Quasinormal modes of scalarized black holes in the Einstein–Maxwell–Scalar theory

We perform the stability analysis on scalarized charged black holes in the Einstein–Maxwell–Scalar (EMS) theory by computing quasinormal mode spectrum. It is noted that the appearance of these black holes with scalar hair is closely related to the instability of Reissner–Nordström black holes without scalar hair in the EMS theory. The scalarized charged black hole solutions are classified by the order number of n=0,1,2,⋯, where n=0 is called the fundamental branch and n=1,2,⋯ denote the n excited branches. Here, we show that the n=1,2 excited black holes are unstable against the s(l=0)-mode scalar perturbation, while the n=0 black hole is stable against all scalar–vector–tensor perturbations. This is consistent with other scalarized black holes without charge found in the Einstein–Scalar–Gauss–Bonnet theory.

Thermodynamics of novel dilatonic BTZ black holes coupled to Born-Infeld electrodynamics

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.

Charged rotating black holes coupled with nonlinear electrodynamics Maxwell field in the mimetic gravity

In mimetic gravity, we derive D-dimension charged black hole solutions having flat or cylindrical horizons with zero curvature boundary. The asymptotic behaviours of these black holes behave as (A)dS. We study both linear and nonlinear forms of the Maxwell field equations in two separate contexts. For the nonlinear case, we derive a new solution having a metric with monopole, dipole and quadrupole terms. The most interesting feature of this black hole is that its dipole and quadruple terms are related by a constant. However, the solution reduces to the linear case of the Maxwell field equations when this constant acquires a null value. Also, we apply a coordinate transformation and derive rotating black hole solutions (for both linear and nonlinear cases). We show that the nonlinear black hole has stronger curvature singularities than the corresponding known black hole solutions in general relativity. We show that the obtained solutions could have at most two horizons. We determine the critical mass of the degenerate horizon at which the two horizons coincide. We study the thermodynamical stability of the solutions. We note that the nonlinear electrodynamics contributes to process a second-order phase transition whereas the heat capacity has an infinite discontinuity.

Overcharging black holes and cosmic censorship in Eddington-inspired Born-Infeld gravity

The Eddington-inspired Born-Infeld (EiBI) gravity is a modification of the theory of general relativity inspired by the nonlinear Born-Infeld electrodynamics. The theory is described by a series of higher curvature terms added to the Einstein-Hilbert action with the parameter $\kappa$. The EiBI gravity has several interesting exact neutral and charged black hole solutions. We study the problem of overcharging extremal black hole solutions of EiBI gravity using a charged test particle to create naked singularity. We show that unlike general relativity, the overcharging could be possible for a charged extremal black hole in EiBI gravity as long as the matter sector is described by usual Maxwell's electrodynamics. Once the matter sector is also modified in accordance to the Born-Infeld prescription with the parameter $b$, the overcharging is not possible as long as the parameters obey the condition $4 \kappa b^2 \leq 1$.

Non-linear charged AdS black hole in massive gravity

In the context of the non-linear electrodynamics and the Einstein-massive gravity, we have obtained a 4hbox {D} non-linear charged AdS black hole solution. Then, we investigated its horizon structure. In addition, the thermodynamics and phase structure of this black hole solution have been studied in details. We have computed various thermodynamic quantities of the black hole, such as the temperature, entropy, the heat capacity at constant pressure, or the Gibbs free energy. The black hole can undergo the first-order, second-order phase transitions which depend crucially on the effective horizon curvature, the sign of the coupling parameter c_1, the characteristic parameter of the non-linear electrodynamics, as well as the pressure. Finally, we derived the equation of state and studied P-V criticality in the case of the positive effective horizon curvature.

Non-commutative inspired black holes in Euler–Heisenberg non-linear electrodynamics

We find non-commutative inspired electrically and magnetically charged black hole solutions in Euler–Heisenberg non-linear electrodynamics. We analyse the weak energy condition and show that it is satisfied in opposition to the commutative case. We also obtain the shadow associated with these metrics that may be susceptible to observation.

Charged and Non-Charged Black Hole Solutions in Mimetic Gravitational Theory

In this study, we derive, in the framework of mimetic theory, charged and non-charged black hole solutions for spherically symmetric as well as flat horizon spacetimes. The asymptotic behavior of those black holes behave as flat or (A)dS spacetimes and coincide with the solutions derived before in general relativity theory. Using the field equations of non-linear electrodynamics mimetic theory we derive new black hole solutions with monopole and quadrupole terms. The quadruple term of those black holes is related by a constant so that its vanishing makes the solutions coincide with the linear Maxwell black holes. We study the singularities of those solutions and show that they possess stronger singularity than the ones known in general relativity. Among many things, we study the horizons as well as the heat capacity to see if the black holes derived in this study have thermodynamical stability or not.