Charged Black Hole Solutions Research Articles

F(R)Gravity’s Rainbow and Its Einstein Counterpart

Motivated by UV completion of general relativity with a modification of a geometry at high energy scale, it is expected to have an energy dependent geometry. In this paper, we introduce charged black hole solutions with power Maxwell invariant source in the context of gravity’s rainbow. In addition, we investigate two classes ofF(R)gravity’s rainbow solutions. At first, we study energy dependentF(R)gravity without energy-momentum tensor, and then we obtainF(R)gravity’s rainbow in the presence of conformally invariant Maxwell source. We study geometrical properties of the mentioned solutions and compare their results. We also give some related comments regarding thermodynamical behavior of the obtained solutions and discuss thermal stability of the solutions.

Charged Einstein-aether black holes and Smarr formula

In the framework of the Einstein-Maxwell-aether theory, we present two new classes of exact charged black hole solutions, which are asymptotically flat and possess the universal as well as Killing horizons. We also construct the Smarr formulas, and calculate the temperatures of the horizons, using the Smarr mass-area relation. We find that, in contrast to the neutral case, such obtained temperature is not proportional to its surface gravity at any of the two kinds of the horizons. Einstein-Maxwell-aether black holes with the cosmological constant and their topological cousins are also given.

Extended phase space thermodynamics and $$P-V$$ P - V criticality of charged black holes in Brans–Dicke theory

In this paper, taking in to account Brans-Dick theory, we investigate thermodynamic behavior of charged black hole solutions. We study the analogy of the black hole solution with the Van der Waals liquid-gas system in the extended phase space by considering the cosmological constant as dynamical pressure. We obtain critical values of thermodynamic coordinates and plot $P-r_{+}$ and $G-T$ diagrams to study the phase transition.

Quartic quasi-topological-Born–Infeld gravity

In this paper, quartic quasi-topological black holes in the presence of a nonlinear electromagnetic Born-Infeld field is presented. By using the metric parameters, the charged black hole solutions of quasi-topological Born-Infeld gravity is considered. The thermodynamics of these black holes are investigated and I show that the thermodynamics and conserved quantities verify the first law of thermodynamics. I also introduce the thermodynamics of asymptotically AdS rotating black branes with flat horizon of these class of solutions and I calculate the finite action by use of the counterterm method inspired by AdS/CFT correspondence.

Black hole solution and strong gravitational lensing in Eddington-inspired Born–Infeld gravity

A new theory of gravity called Eddington-inspired Born-Infeld (EiBI) gravity was recently proposed by Ba\~{n}ados and Ferreira. This theory leads to some exciting new features, such as free of cosmological singularities. In this paper, we first obtain a charged EiBI black hole solution with a nonvanishing cosmological constant when the electromagnetic field is included in. Then based on it, we study the strong gravitational lensing by the asymptotic flat charged EiBI black hole. The strong deflection limit coefficients and observables are shown to closely depend on the additional coupling parameter $\kappa$ in the EiBI gravity. It is found that, compared with the corresponding charged black hole in general relativity, the positive coupling parameter $\kappa$ will shrink the black hole horizon and photon sphere. Moreover, the coupling parameter will decrease the angular position and relative magnitudes of the relativistic images, while increase the angular separation, which may shine new light on testing such gravity theory in near future by the astronomical instruments.

Charged Galileon black holes

We consider an Abelian gauge field coupled to a particular truncation of Horndeski theory. The Galileon field has translation symmetry and couples non minimally both to the metric and the gauge field. When the gauge-scalar coupling is zero the gauge field reduces to a standard Maxwell field. By taking into account the symmetries of the action, we construct charged black hole solutions. Allowing the scalar field to softly break symmetries of spacetime we construct black holes where the scalar field is regular on the black hole event horizon. Some of these solutions can be interpreted as the equivalent of Reissner-Nordstrom black holes of scalar tensor theories with a non trivial scalar field. A self tuning black hole solution found previously is extended to the presence of dyonic charge without affecting whatsoever the self tuning of a large positive cosmological constant. Finally, for a general shift invariant scalar tensor theory we demonstrate that the scalar field Ansatz and method we employ are mathematically compatible with the field equations. This opens up the possibility for novel searches of hairy black holes in a far more general setting of Horndeski theory.

Effects of cosmic acceleration on black hole thermodynamics

Direct local impacts of cosmic acceleration upon a black hole are matters of interest. Babichev et al. had published before that the Friedmann equations which are prevailing the part of fluid filled up in the universe to lead (or to be very specific, ‘dominate’) the other constituents of universe and are forcing the universe to undergo present-day accelerating phase (or to lead to violate the strong energy condition and latter the week energy condition), will themselves tell that the rate of change of mass of the central black hole due to such exotic fluid’s accretion will essentially shrink the mass of the black hole. But this is a global impact indeed. The local changes in the space time geometry next to the black hole can be analysed from a modified metric governing the surrounding space time of a black hole. A charged de Sitter black hole solution encircled by quintessence field is chosen for this purpose. Different thermodynamic quantities are analysed for different values of quintessence equation of state parameter, ω q . Specific jumps in the nature of the thermodynamic space near to the quintessence or phantom barrier are noted and physically interpreted as far as possible. Nature of phase transitions and the situations at which these transitions are taking place are also explored. It is determined that before quintessence starts to work ( $\omega_{q}=-0.33>-\frac{1}{3}$ ) it was preferable to have a small unstable black hole followed by a large stable one. But in quintessence ( $-\frac{1}{3}>\omega_{q}>-1$ ), black holes are destined to be unstable large ones pre-quelled by stable/unstable small/intermediate mass black holes.

Thermodynamics of charged Lifshitz black holes with quadratic corrections

In arbitrary dimension, we consider the Einstein-Maxwell Lagrangian supplemented by the more general quadratic-curvature corrections. For this model, we derive four classes of charged Lifshitz black hole solutions for which the metric function is shown to depend on a unique integration constant. The masses of these solutions are computed using the quasilocal formalism based on the relation established between the off-shell ADT and Noether potentials. Among these four solutions, three of them are interpreted as extremal in the sense that their mass vanishes identically. For the last family of solutions, the quasilocal mass and the electric charge both are shown to depend on the integration constant. Finally, we verify that the first law of thermodynamics holds for each solution and a Smarr formula is also established for the four solutions.

Noncommutative geometry inspired $$3$$ 3 -dimensional charged black hole solution in an anti-de Sitter background spacetime

We report a 3D charged black hole solution in an anti desetter space inspired by noncommutative geometry.In this construction,the black hole exhibits two horizon which turn into a single horizon in the extreme case.We investigate the impacts of the electromagnetic field on the location of the event horizon,mass and thermodynamic properties such as Hawking temperature,entropy and heat capacity of the black hole.The geodesics of the charged black hole are also analyzed.

Thermodynamics of black holes in massive gravity

We present a class of charged black hole solutions in an ($n+2)$-dimensional massive gravity with a negative cosmological constant, and study thermodynamics and phase structure of the black hole solutions both in grand canonical ensemble and canonical ensemble. The black hole horizon can have a positive, zero or negative constant curvature characterized by constant $k$. By using Hamiltonian approach, we obtain conserved charges of the solutions and find black hole entropy still obeys the area formula and the gravitational field equation at the black hole horizon can be cast into the first law form of black hole thermodynamics. In grand canonical ensemble, we find that thermodynamics and phase structure depends on the combination $k -\mu^2/4 +c_2 m^2$ in the four dimensional case, where $\mu$ is the chemical potential and $c_2m^2$ is the coefficient of the second term in the potential associated with graviton mass. When it is positive, the Hawking-Page phase transition can happen, while as it is negative, the black hole is always thermodynamically stable with a positive capacity. In canonical ensemble, the combination turns out to be $k+c_2m^2$ in the four dimensional case. When it is positive, a first order phase transition can happen between small and large black holes if the charge is less than its critical one. In higher dimensional ($n+2 \ge 5$) case, even when the charge is absent, the small/large black hole phase transition can also appear, the coefficients for the third ($c_3m^2$) and/or the fourth ($c_4m^2$) terms in the potential associated with graviton mass in the massive gravity can play the same role as the charge does in the four dimensional case.

Extremal hairy black holes

We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and an U(1) electromagnetic field. Solving the coupled Einstein-Maxwell-scalar system we find exact hairy charged black hole solutions with the scalar field regular everywhere. We go to the zero temperature limit and we study the effect of the scalar field on the near horizon geometry of an extremal black hole. We find that except a critical value of the charge of the black hole there is also a critical value of the charge of the scalar field beyond of which the extremal black hole is destabilized. We study the thermodynamics of these solutions and we find that if the space is flat then at low temperature the Reissner-Nordstr\"om black hole is thermodynamically preferred, while if the space is AdS the hairy charged black hole is thermodynamically preferred at low temperature.

Black hole solutions in Chern-Simons AdS supergravity

We study charged AdS black hole solutions in five-dimensional Chern-Simons supergravity. The minimal supergroup containing such AdSxU(1) configurations is the superunitary group SU(2,2|N). For this model, we find analytic black hole solutions that asymptote to locally AdS spacetime at the boundary. A solution can carry U(1) charge provided the spacetime torsion is non-vanishing. Thus, we analyze the most general configuration consistent with the local AdS isometries in Riemann-Cartan space. The coupling of torsion in the action resembles that of the universal axion of string theory, and it is ultimately due to this field that the theory acquires propagating degrees of freedom. Through a careful analysis of the canonical structure the local degrees of freedom of the theory are identified in the static symmetric sector of phase space.

Black brane solutions governed by fluxbrane polynomials

A family of composite black brane solutions in the model with scalar fields and fields of forms is presented. The metric of any solution is defined on a manifold which contains a product of several Ricci-flat "internal" spaces. The solutions are governed by moduli functions H_s (s = 1, ..., m) obeying non-linear differential equations with certain boundary conditions imposed. These master equations are equivalent to Toda-like equations and depend upon the non-degenerate (m x m) matrix A. It was conjectured earlier that the functions H_s should be polynomials if A is a Cartan matrix for some semisimple finite-dimensional Lie algebra (of rank m). It is shown that the solutions to master equations may be found by using so-called fluxbrane polynomials which can be calculated (in principle) for any semisimple finite-dimensional Lie algebra. Examples of dilatonic charged black hole (0-brane) solutions related to Lie algebras A_1, A_2, C_2 and G_2 are considered.

A class of charged black hole solutions in massive (bi)gravity

We present a new class of solutions describing charged black holes in massive (bi)gravity. For a generic choice of the parameters of the massive gravity action, the solution is the Reissner-Nordström-de Sitter metric written in the Eddington-Finkelstein coordinates for both metrics. We also study a special case of the parameters, for which the space of solutions contains an extra symmetry.

Static black holes and strictly static spacetimes in Einstein-Gauss-Bonnet gravity with gauge field

We examine strictly static asymptotically flat spacetimes in Einstein-Gauss-Bonnet gravity with U(1) gauge field, revealing that, up to small curvature corrections, confomally flat slices of the spacetime in question are of Minkowski origin. We consider uncharged and charged black hole solutions in the theory, showing that, up to the small curvature limit, they are diffeomorphic to Schwarzschild_Tangherlini or Reissner-Nordstrom solutions, respectively.

Nonlinearly charged Lifshitz black holes for any exponent z > 1

Charged Lifshitz black holes for the Einstein-Proca-Maxwell system with a negative cosmological constant in arbitrary dimension D are known only if the dynamical critical exponent is fixed as z = 2(D − 2). In the present work, we show that these configurations can be extended to much more general charged black holes which in addition exist for any value of the dynamical exponent z > 1 by considering a nonlinear electrodynamics instead of the Maxwell theory. More precisely, we introduce a two-parametric nonlinear electrodynamics defined in the more general, but less known, so-called ( $ \mathcal{H} $ , P )-formalism and obtain a family of charged black hole solutions depending on two parameters. We also remark that the value of the dynamical exponent z = D − 2 turns out to be critical in the sense that it yields asymptotically Lifshitz black holes with logarithmic decay supported by a particular logarithmic electrodynamics. All these configurations include extremal Lifshitz black holes. Charged topological Lifshitz black holes are also shown to emerge by slightly generalizing the proposed electrodynamics.

Dilaton black holes coupled to nonlinear electrodynamic field

The theory of nonlinear electrodynamics has got a lot of attentions in recent years. It was shown that Born-Infeld nonlinear electrodynamics is not the only modification of the linear Maxwell's field which keeps the electric field of a charged point particle finite at the origin, and other type of nonlinear Lagrangian such as exponential and logarithmic nonlinear electrodynamics can play the same role. In this paper, we generalize the study on the exponential nonlinear electrodynamics by adding a scalar dilaton field to the action. By suitably choosing the coupling of the matter field to the dilaton field, we vary the action and obtain the corresponding field equations. Then, by making a proper ansatz, we construct a new class of charged dilaton black hole solutions coupled to the exponential nonlinear electrodynamics field in the presence of two Liouville-type potentials for the dilaton field. Due to the presence of the dilaton field, the asymptotic behavior of these solutions are neither flat nor (A)dS. In the limiting case where the nonlinear parameter $\beta^2$ goes to infinity, our solution reduces to the Einstein-Maxwell dilaton black holes. We obtain the mass, temperature, entropy and electric potential of these solutions. We also study the behaviour of the electric field as well as the electric potential of these black holes near the origin. We find that the electric field has a finite value \textit{near} the origin, which is the same as the electric field of Born-Infeld nonlinear electrodynamics, but it can diverge exactly at $r=0$ depending on the model parameters. We also investigate the effects of the dilaton field on the behaviour of the electric field and electric potential. Finally, we check the validity of the first law of black hole thermodynamics on the black hole horizon.

Study of Confinement/Deconfinement Transition in AdS/QCD with Generalized Warp Factors

We study analytical solutions of charged black holes and thermally charged AdS with generalized warped factors in Einstein-Maxwell-Dilaton system. We calculate Euclidean action for charged AdS and thermally charged AdS. The actions in both backgrounds are regularized by the method of background subtraction. The study of phase transition between charged black hole and thermally charged AdS gives an insight into the confinement/deconfinement transition. The plots of grand potential versus temperature and chemical potential versus transition temperature are obtained.

The Geometry of Black Hole Singularities

Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to make Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.

Extended phase space thermodynamics andP−Vcriticality of black holes with a nonlinear source

In this paper, we consider the solutions of Einstein gravity in the presence of a generalized Maxwell theory, namely power Maxwell invariant. First, we investigate the analogy of nonlinear charged black hole solutions with the Van der Waals liquid--gas system in the extended phase space where the cosmological constant appear as pressure. Then, we plot isotherm $P$--$V$ diagram and study the thermodynamics of AdS black hole in the (grand canonical) canonical ensemble in which (potential) charge is fixed at infinity. Interestingly, we find the phase transition occurs in the both of canonical and grand canonical ensembles in contrast to RN black hole in Maxwell theory which only admits canonical ensemble phase transition. Moreover, we calculate the critical exponents and find their values are the same as those in mean field theory. Besides, considerably, we find in the grand canonical ensembles universal ratio $\frac{P_{c}v_{c}}{T_{c}}$ is independent of spacetime dimensions.