Charged Black Hole Solutions Research Articles

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.

Asymptotically AdS charged black holes in string theory with Gauss-Bonnet correction in various dimensions

We study charged black hole solutions in Einstein-Maxwell-Gauss-Bonnet theory with the dilaton field which is the low-energy effective theory of the heterotic string. The spacetime is $D$ dimensional and assumed to be static and plane symmetric with the ($D\ensuremath{-}2$)-dimensional constant curvature space and asymptotically anti--de Sitter. By imposing the boundary conditions of the existence of the regular black hole horizon and proper behavior at infinity where the Breitenlohner-Freedman bound should be satisfied, we construct black hole solutions numerically. We give the relations among the physical quantities of the black holes such as the horizon radius, the mass, the temperature, and so on. The properties of the black holes do not depend on the dimensions qualitatively, which is different from the spherically symmetric and asymptotically flat case. There is nonzero lower limit for the radius of the event horizon below which no solution exists. The temperature of the black hole becomes smaller as the horizon radius is smaller but remains nonzero when the lower limit is attained.

Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics

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 families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal "renormalization group"-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics...

Charged D3-D7 plasmas: novel solutions, extremality and stability issues

We study finite temperature N=4 Super Yang-Mills (and more general gauge theories realized on intersecting D3-D7 branes) in the presence of dynamical massless fundamental matter fields at finite baryon charge density. We construct the holographic dual charged black hole solutions at first order in the flavor backreaction but exact in the charge density. The thermodynamical properties of the dual gauge theories coincide with the ones found in the usual charged D7-probe limit and the system turns out to be thermodynamically stable. By analyzing the higher order correction in the flavor backreaction, we provide a novel argument for the un-reliability of the charged probe approximation (and the present solution) in the extremality limit, i.e. at zero temperature. We then consider scalar mesonic-like bound states, whose spectrum is dual to that of linearized fluctuations of D7-brane worldvolume fields around our gravity backgrounds. In particular we focus on a scalar field saturating the Breitenlohner-Freedman bound in the flavorless limit, and coupled to fields dual to irrelevant operators. By looking at quasinormal modes of this scalar, we find no signals of instabilities in the regime of validity of the solutions.

Charged black holes in nonlinear massive gravity

We find static charged black hole solutions in nonlinear massive gravity. In the parameter space of two gravitational potential parameters $(\ensuremath{\alpha},\ensuremath{\beta})$ we show that below the Compton wavelength the black hole solutions reduce to that of Reissner-Nordstr\"om via the Vainshtein mechanism in the weak-field limit. In the simplest case with $\ensuremath{\alpha}=\ensuremath{\beta}=0$ the solution exhibits the van Dam-Veltman-Zakharov discontinuity but ordinary general relativity is recovered deep inside the horizon due to the existence of electric charge, though this case is observationally excluded. For $\ensuremath{\alpha}\ensuremath{\ne}0$ and $\ensuremath{\beta}=0$, the post-Newtonian parameter of the charged black hole evolves to that of general relativity via the Vainshtein mechanism within a macroscopic distance; however, a logarithmic correction to the metric factor of the time coordinate is obtained. When $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ are both nonzero, there exist two branches of solutions depending on the positivity of $\ensuremath{\beta}$. When $\ensuremath{\beta}<0$, the strong coupling of the scalar graviton weakens gravity at distances smaller than the Vainshtein radius. However, when $\ensuremath{\beta}>0$ the metric factors exhibit only small corrections compared to the solutions obtained in general relativity, and under a particular choice of $\ensuremath{\beta}={\ensuremath{\alpha}}^{2}/6$ the standard Reissner-Nordstr\"om-de Sitter solution is recovered.

Semi-local quantum criticality in string/M-theory

Semi-local quantum critical behaviour in $D-1$ spacetime dimensions can be holographically described by metrics that are conformal to $AdS_2\times\mathbb{R}^{D-2}$, with the conformal factor characterised by a parameter $\eta$. We analyse such "$\eta$-geometries" in a top-down setting by focussing on the $U(1)^4$ truncation of D=4 N=8 gauged supergravity. The model has extremal black hole solutions carrying three non-zero electric or magnetic charges which approach $AdS_4$ in the UV and an $\eta=1$ geometry in the IR. Adding a fourth charge provides a mechanism to resolve the singularity of the $\eta$-geometry, replacing it with an $AdS_2\times\mathbb{R}^2$ factor in the IR, while maintaining a large region where the $\eta$-geometry scaling is approximately valid. Some of the magnetically charged black hole solutions preserve supersymmetry while others just preserve it in the IR. Finally, we show that $\eta$-geometries, with various values of $\eta$, can be obtained from the dimensional reduction of geometries consisting of $AdS$ or Lifshitz geometries with flat directions.

Exact charged black-hole solutions in D-dimensional f (T) gravity: torsion vs curvature analysis

AbstractWe extract exact charged black-hole solutions with flat transverse sections in the framework of D-dimensional Maxwell-f(T) gravity, and we analyze the singularities and horizons based on both torsion and curvature invariants. Interestingly enough, we find that in some particular solution subclasses there appear more singularities in the curvature scalars than in the torsion ones. This difference disappears in the uncharged case, or in the case wheref(T) gravity becomes the usual linear-in-Tteleparallel gravity, that is General Relativity. Curvature and torsion invariants behave very differently when matter fields are present, and thusf(R) gravity andf(T) gravity exhibit different features and cannot be directly re-casted each other.

Instability of charged Lovelock black holes: Vector perturbations and scalar perturbations

We examine the stability of charged Lovelock black hole solutions under vector type and scalar type perturbations. We find the suitable master variables for the stability analysis; the equations for these variables are the Schrodinger type equations with two components and these Schrodinger operators are symmetric. By these master equations, we show that charged Lovelock Black holes are stable under vector type perturbations. For scalar type perturbations, we show the criteria for the instability and check these numerically. In our previous paper, we have shown that nearly extremal black holes have the instability under tensor type perturbations. In this paper, we find that black holes with small charge have the instability under scalar type perturbations even if they have relatively large mass.

Phase transition and scaling behavior of topological charged black holes in Hořava–Lifshitz gravity

Gravity can be thought as an emergent phenomenon and it has a nice ‘thermodynamic’ structure. In this context, it is then possible to study the thermodynamics without knowing the details of the underlying microscopic degrees of freedom. Here, based on the ordinary thermodynamics, we investigate the phase transition of the static, spherically symmetric charged black hole solution with the arbitrary scalar curvature 2k in Hořava–Lifshitz gravity at the Lifshitz point z = 3. The analysis is done using the canonical ensemble framework, i.e. the charge is kept fixed. We find (a) for both k = 0 and k = 1, there is no phase transition, (b) while k = −1 case exhibits the second-order phase transition within the physical region of the black hole. The critical point of second-order phase transition is obtained by the divergence of the heat capacity at constant charge. Near the critical point, we find the various critical exponents. It is also observed that they satisfy the usual thermodynamic scaling laws.

Charged black holes in string theory with Gauss-Bonnet correction in various dimensions

We study charged black hole solutions in Einstein-Gauss-Bonnet theory with the dilaton field which is the low-energy effective theory of the heterotic string. The spacetime is $D$-dimensional and assumed to be static and spherically symmetric with the ($D\ensuremath{-}2$)-dimensional constant curvature space and asymptotically flat. The system of the basic equations is complex and the solutions are obtained numerically. We identify the allowed parameter region where the black hole solutions exist, and show configurations of the field functions in $D=4--6$ and 10. We also show the relations of the physical quantities of the black holes such as the horizon radius, the mass, the temperature, and so on, and find several results. The forms of the allowed parameter regions are different depending on the dimension. There is no extreme black hole solution with $T=0$ that can be obtained by taking the limit of the nonextreme solutions within the parameter range we chose. Entropy of the black holes in the dilatonic theory is always larger than that in the nondilatonic theory. Our analysis includes the higher order term of the dilaton field which is not in our previous works. Its effect remarkably appears in five dimensions and is given in the Appendix. By our analysis it is found that the properties of the black hole solutions strongly depend on the dimension, charge, existence of the dilaton field. Hence both the detailed analyses of the individual systems and the investigations from the systematic point of view are important.

New solutions of charged regular black holes and their stability

We construct new regular black hole solutions by matching the de Sitter solution and the Reissner-Nordstrom solution with a timelike thin shell. The thin shell is assumed to have mass but no pressure and obeys an equation of motion derived from Israel's junction conditions. By investigating the equation of motion for the shell, we obtain stationary solutions of charged regular black holes and examine stability of the solutions. Stationary solutions are found in limited ranges of 0.87L < m < 1.99L, and they are stable against small radial displacement of the shell with fixed values of m, M, and Q if M>0, where L is the de Sitter horizon radius, m the black hole mass, M the proper mass of the shell and Q the black hole charge. All the solutions obtained are highly charged in the sense of Q/m >0.866. By taking the massless limit of the shell in the present regular black hole solutions, we obtain the charged regular black hole with a massless shell obtained by Lemos and Zanchin and investigate stability of the solutions. It is found that Lemos and Zanchin's regular black hole solutions given by the massless limit of the present regular black hole solutions permit stable solutions, which are obtained by the limit of M -> 0.

Black holes dual to helical current phases

We consider the class of $d=4$ conformal field theories at finite temperature and chemical potential that are holographically described within $D=5$ Einstein-Maxwell theory with a Chern-Simons term. The high temperature phase, which is spatially homogeneous and isotropic, is dual to the AdS-Reissner-N\"ordstrom black brane solution. For sufficiently large Chern-Simons coupling, we construct new electrically charged AdS black hole solutions that are dual to the low temperature, spatially modulated phase. In this phase the current, associated with the Abelian global symmetry, spontaneously acquires a helical order. The new black holes are stationary and also have Bianchi ${\mathrm{VII}}_{0}$ symmetry.

Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography

AbstractWe consider a general Kaluza-Klein reduction of a truncated Lovelock theory. We find necessary geometric conditions for the reduction to be consistent. The resulting lower-dimensional theory is a higher derivative scalar-tensor theory, depends on a single real parameter and yields second-order field equations. Due to the presence of higher-derivative terms, the theory has multiple applications in modifications of Einstein gravity (Galileon/Horndesky theory) and holography (Einstein-Maxwell-Dilaton theories). We find and analyze charged black hole solutions with planar or curved horizons, both in the ‘Einstein’ and ‘Galileon’ frame, with or without cosmological constant. Naked singularities are dressed by a geometric event horizon originating from the higher-derivative terms. The near-horizon region of the near-extremal black hole is unaffected by the presence of the higher derivatives, whether scale invariant or hyperscaling violating. In the latter case, the area law for the entanglement entropy is violated logarithmically, as expected in the presence of a Fermi surface. For negative cosmological constant and planar horizons, thermodynamics and first-order hydrodynamics are derived: the shear viscosity to entropy density ratio does not depend on temperature, as expected from the higher-dimensional scale invariance.

Charged quantum black holes: thermal stability criterion

A criterion of thermal stability is derived for electrically charged quantum black holes having a large horizon area (compared to the Planck area), as an inequality between the mass of the black hole and its microcanonical entropy. The derivation is based on the key results of loop quantum gravity and equilibrium statistical mechanics of a grand canonical ensemble, with Gaussian fluctuations around an equilibrium thermal configuration assumed here to be a quantum isolated horizon. No aspect of classical black hole geometry is used to deduce the stability criterion. Since no particular form of the mass function is used a priori, our stability criterion provides a platform to test the thermal stability of a black hole with a given mass function. The mass functions of the two most familiar charged black hole solutions are tested as a fiducial check. We also discuss the validity of the saddle-point approximation used to incorporate thermal fluctuations. Moreover, the equilibrium Hawking temperature is shown to have an additional quantum correction over the semiclassical value.

A rotating charged black hole solution in f(R) gravity

In the context of f(R) theories of gravity, we address the problem of finding a rotating charged black hole solution in the case of constant curvature. A new metric is obtained by solving the field equations and we show that its behaviour is typical of a rotating charged source. In addition, we analyse the thermodynamics of the new black hole. The results ensure that the thermodynamical properties in f(R) gravities are qualitatively similar to those of standard General Relativity.

Inhomogeneous charged black hole solutions in asymptotically anti-de Sitter spacetime

We investigate static inhomogeneous charged planar black hole solutions of the Einstein-Maxwell system in an asymptotically anti-de Sitter spacetime. Within the framework of linear perturbations, the solutions are numerically and analytically constructed from the Reissner-Nordstr\"{o}m-AdS black hole solution. The perturbation analysis predicts that the Cauchy horizon always disappears for any wavelength perturbation, supporting the strong cosmic censorship conjecture. For extremal black holes, we analytically show that an observer freely falling into the black hole feels infinite tidal force at the horizon for any long wavelength perturbation, even though the Kretschmann scalar curvature invariant remains small.

Asymptotic charged BTZ black hole solutions

The well-known $(2+1)$-dimensional Reissner-Nordstrom (BTZ) black hole can be generalized to three dimensional Einstein-nonlinear electromagnetic field, motivated from obtaining a finite value for the self-energy of a pointlike charge. Considering three types of nonlinear electromagnetic fields coupled with Einstein gravity, we derive three kinds of black hole solutions which their asymptotic properties are the same as charged BTZ solution. In addition, we calculate conserved and thermodynamic quantities of the solutions and show that they satisfy the first law of thermodynamics. Finally, we perform a stability analysis in the canonical ensemble and show that the black holes are stable in the whole phase space.

Thermodynamics of black holes in Einstein-Gauss-Bonnet AdS gravity coupled to Nonlinear Electrodynamics

In an arbitrary dimension D, we study quadratic corrections to Einstein-Hilbert action described by the Gauss-Bonnet term. We consider charged black hole solutions with anti-de Sitter (AdS) asymptotics, of interest in the context of gravity/gauge theory dualities (AdS/CFT). The electric charge here is due to the addition of an arbitrary nonlinear electrodynamics (NED) Lagrangian. Due to the existence of a vacuum energy for global AdS spacetime in odd dimensions in the framework of AdS/CFT correspondence, we derive a Quantum Statistical Relation directly from the Euclidean action and not from the First Law of thermodynamics. To this end, we employ a background-independent regularization scheme which consists in supplementing the bulk action with counterterms that depend both on the extrinsic and intrinsic curvatures of the boundary (also known as Kounterterms). This procedure results in a consistent inclusion of the vacuum energy in the thermodynamic description for Einstein-Gauss-Bonnet AdS gravity regardless the explicit form of the NED Lagrangian.

Extremal charged black holes with a twisted extra dimension

We construct odd-dimensional extremal charged black hole solutions with a twisted S^1 as an extra dimension on generalized Euclidean Taub-NUT spaces. There exists a null hypersurface where an expansion for an outgoing null geodesic congruence vanishes, then these spacetimes look like black holes. We show that the metrics admit C^0 extension across the horizon, but some components of Riemann curvature diverge there if the dimension is higher than five. The singularity is not much strong so that an observer along a free-fall geodesic can traverse the horizon. We also show solutions with a positive cosmological constant.

General nonextremal rotating charged AdS black holes in five-dimensional [formula omitted] gauged supergravity: A simple construction method

With the help of a generalized form of the metric ansatz found for the single-charge case in a previous work [S.Q. Wu, Phys. Rev. D 83 (2011) 121502(R)], I adopt a simple algorithm to construct the most general nonextremal rotating charged black hole solutions in five-dimensional U(1)3 gauged supergravity. The general solution that is interesting for testing the AdS5/CFT4 correspondence in M-theory, is characterized by its mass, two unequal rotation parameters, three different U(1) charges, and a negative cosmological constant. The metric ansatz is very universal and illuminative, it is not only especially suitable for constructing solutions with multiple different electric charges in (un)gauged supergravities, but also for other dilatonic gravity theory.