Charged Hairy Black Hole Research Articles

Black Holes with Electroweak Hair.

We construct static and axially symmetric magnetically charged hairy black holes in the gravity-coupled Weinberg-Salam theory. Large black holes merge with the Reissner-Nordström (RN) family, while the small ones are extremal and support a hair in the form of a ring-shaped electroweak condensate carrying superconducting W currents and up to 22% of the total magnetic charge. The extremal solutions are asymptotically RN with a mass below the total charge, M<|Q|, due to the negative Zeeman energy of the condensate interacting with the black hole magnetic field. Therefore, they cannot decay into RN black holes. As their charge increases, they show a phase transition when the horizon symmetry changes from spherical to oblate. At this point they have the mass typical for planetary size black holes of which ≈11% is stored in the hair. Being obtained within a well-tested theory, our solutions are expected to be physically relevant.

Violent Nonlinear Collapse in the Interior of Charged Hairy Black Holes

We construct a new one-parameter family, indexed by ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon $$\\end{document}, of two-ended, spatially-homogeneous black hole interiors solving the Einstein–Maxwell–Klein–Gordon equations with a (possibly zero) cosmological constant Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} and bifurcating off a Reissner–Nordström-(dS/AdS) interior (ϵ=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon =0$$\\end{document}). For all small ϵ≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon \ e 0$$\\end{document}, we prove that, although the black hole is charged, its terminal boundary is an everywhere-spacelike Kasner singularity foliated by spheres of zero radius r. Moreover, smaller perturbations (i.e. smaller |ϵ|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\epsilon |$$\\end{document}) are more singular than larger ones, in the sense that the Hawking mass and the curvature blow up following a power law of the form r-O(ϵ-2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r^{-O(\\epsilon ^{-2})}$$\\end{document} at the singularity {r=0}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\{r=0\\}$$\\end{document}. This unusual property originates from a dynamical phenomenon—violent nonlinear collapse—caused by the almost formation of a Cauchy horizon to the past of the spacelike singularity {r=0}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\{r=0\\}$$\\end{document}. This phenomenon was previously described numerically in the physics literature and referred to as “the collapse of the Einstein–Rosen bridge”. While we cover all values of Λ∈R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda \\in \\mathbb {R}$$\\end{document}, the case Λ<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda <0$$\\end{document} is of particular significance to the AdS/CFT correspondence. Our result can also be viewed in general as a first step towards the understanding of the interior of hairy black holes.

Existence of thermodynamically stable asymptotically flat black holes

We use the quasilocal formalism of Brown and York, supplemented with counterterms, to investigate the thermodynamics of asymptotically flat black holes. We consider two families of exact regular black hole solutions, which are thermodynamically stable. The first one consists of four-dimensional static charged hairy black holes in extended supergravity. The second family consists of five-dimensional static charged black holes in Gauss-Bonnet (GB) gravity. Despite the fact that their characteristics are completely different, we found a striking similarity between their thermodynamic behavior. Published by the American Physical Society 2024

Superradiance instabilities of charged black holes in Einstein-Maxwell-scalar theory

We study time evolutions of charged scalar perturbations on the background of a charged hairy black hole, in which the perturbations can be governed by a double-peak effective potential. By extracting quasinormal modes from the waveform of scalar perturbations, we discover that some quasinormal modes, which are trapped in a potential well between two potential peaks, can be superradiantly amplified. These superradiant modes make the hairy black hole unstable against charged scalar perturbations. Moreover, it is found that the superradiant modes arise from the competition between the superradiant amplification caused by tunneling through the outer potential barrier and the leakage of modes through the inner potential barrier into the black hole.

Charged hairy black holes in the gauged Einstein-Friedberg-Lee-Sirlin model

We obtain charged spherically symmetric black holes in the two-component scalar Einstein-Maxwell-Friedberg-Lee-Sirlin model with a symmetry breaking potential. These asymptotically flat black holes carry resonant scalar Q-hair. As expected, these hairy black holes give rise to non-uniqueness. When comparing these solutions with the corresponding charged boson stars and Reissner-Nordstr\"om black holes, we find a different pattern in the case of a massive real scalar component and a massless one. We demonstrate that, as the real component becomes massless, the resonant hairy black holes bifurcate from Reissner-Nordstr\"om black holes for sufficiently small gravitational coupling.

New phases of mathcal{N} = 4 SYM at finite chemical potential

We do a systematic search of supergravity solutions that, via the AdS5/CFT4 correspondence, are dual to thermal states in mathcal{N} = 4 SYM at finite chemical potential. These solutions dominate the microcanonical ensemble and are required to ultimately reproduce the microscopic entropy of AdS black holes. Using a mix of analytical and numerical methods, we construct and study static charged hairy solitonic and black hole solutions with global AdS5 asymptotics. They are constructed in two distinct consistent truncations of five dimensional gauged supergravity (and can thus be uplifted to asymptotically AdS5×S5 solutions of type IIB supergravity). In the “single charge” truncation which consists of one charged scalar field, hairy black holes exist above a critical charge and merge with the known Behrndt-Cvetič-Sabra (BCS) black holes along a curve determined by the onset of superradiance in the latter family. The lowest mass hairy black hole is a singular zero entropy soliton. In the “two charge” truncation which consists of a two equal charged scalar fields, hairy black holes exist for all charges and merge with the known BCS black holes along their superradiant onset curve. The lowest mass hairy black hole is a smooth supersymmetric zero entropy soliton. Together with the known phases of the truncation with three equal charges, our findings permit a good understanding of the full phase space of SYM thermal states with three arbitrary chemical potentials.

Descalarization by quenching charged hairy black hole in asymptotically AdS spacetime

In this work, we study the real-time dynamics of the charged hairy black hole with the time-dependent source of scalar field in asymptotically anti-de Sitter (AdS) spacetime. The numerical results reveal a novel descalarization mechanism. In order to obtain the hairy black hole as the initial data for the quench process, we first analyze the quasi-normal modes of the massive complex scalar field on the Reissner-Nordström anti-de Sitter (RN-AdS) black hole background. We find the dominant unstable modes for large and small RN-AdS black holes come from the zero-damped modes and AdS modes, respectively. Then, the unstable RN-AdS black holes are perturbed to trigger the transition to hairy black holes. With the hairy black hole in hand, we specify a time dependent scalar source for the system. As the source is turned on, the electric charge, energy and scalar condensation of the system start to oscillate with the entropy increasing monotonically. Finally, with the decay of the scalar source, the system gradually settles down to a new state. Interestingly, the final state of the evolution could be a hairy black hole with less scalar condensation, a RN-AdS black hole or a Schwarzschild-AdS black hole, which depends on the quench strength. However, as long as the quench strength is large enough, the system always loses all the electric charge and converges to the Schwarzschild-AdS black hole.

Magnetically charged Euler-Heisenberg black holes with scalar hair

We study the Einstein-Euler-Heisenberg theory in the presence of a self interacting scalar field, minimally coupled to gravity. We solve analytically the field equations for the magnetically charged case and we obtain novel magnetically charged hairy black holes. The scalar field dresses the black hole with a secondary scalar hair. The hairy black hole develops three horizons when Euler-Heisenberg parameter and the magnetic charge are small and the horizon radius is getting large when the scalar charge and the gravitational mass are large. The presence of matter and the magnetic field outside the horizon of the black hole increases the temperature only for small black holes. Calculating the heat capacity we show that the asymptotically AdS Euler-Heisenberg hairy black hole undergoes a second order phase transition and then it is stabilized. Also the weak energy condition is violated for the asymptotically AdS Euler-Heisenberg hairy black hole.

Probing inside a charged hairy black hole in massive gravity

In this paper, we investigate the internal structure of a charged hairy black hole solution in the non-linear massive gravity. We first consider the impact of various configurations of massive gravity on the condensate operator and then probe the black hole interior dynamics. Like a standard holographic superconductor system, just below the critical temperature, the interior evolves through several distinct epochs, including a collapse of the Einstein-Rosen bridge, Josephson oscillations of the scalar field, and finally a Kasner (or Kasner inversion) cosmology. However, for the large massive gravity parameter, we see distinguishing features for the interior dynamics. In this regime, at a given temperature, the Einstein-Rosen bridge collapse and subsequent Josephson oscillations epochs completely disappear from the interior dynamics and the final Kasner cosmology epoch starts exactly after the would-be inner horizon and the system does not experience the Kasner inversion epoch.

The temperature and entropy corrections of the charged hairy black holes

This paper is devoted to analyzing the consequence of the presence of a scalar field on the statistical properties of the hairy black holes in 2+1 dimensions. The presence of the scalar field can be related to the fluctuations of thermal effects. Consequences of the entropy and temperature corrections, on the statistical characteristics of the black holes investigated. Different types of hairy black holes are considered and their modified thermodynamics quantities are calculated up to the first-orders corrections. The model has some novel outcomes on the P−V plane of space and its features as the phase shifts and critical points. These significant effects are studied, and special attention is paid to checking the local and global steadiness of the black holes under the applied conditions. The influences of the model on the related thermodynamic characteristics are obtained and explained.

Exact topological charged hairy black holes in AdS space in d dimensions

We present a new family of topological charged hairy black hole solutions in asymptotically AdS space in $D$-dimensions. We solve the coupled Einstein-Maxwell-Scalar gravity system and obtain exact charged hairy black hole solutions with planar, spherical and hyperbolic horizon topologies. The scalar field is regular everywhere. We discuss the thermodynamics of the hairy black hole and find drastic changes in its thermodynamic structure due to the scalar field. For the case of planar and spherical horizons, we find charged hairy/RN-AdS black hole phase transition, with thermodynamically preferred and stable charged hairy phases at low temperature. For the case of hyperbolic horizon, no such transition occurs and RN-AdS black holes are always thermodynamically favoured.

New five-dimensional Bianchi type magnetically charged hairy topological black hole solutions in string theory

We construct black hole solutions to the leading order of string effective action in five dimensions with the source given by dilaton and magnetically charged antisymmetric gauge B-field. Presence of the considered B-field leads to the unusual asymptotic behavior of the solutions which are neither asymptotically flat nor asymptotically (A)dS. We consider the three-dimensional space part to correspond to the Bianchi classes and so the horizons of these topological black hole solutions are modeled by seven homogeneous Thurston’s geometries of E^3, S^3, H^3, H^2 times E^1, widetilde{{SL_2R}}, nilgeometry, and solvegeometry. Calculating the quasi-local mass, temperature, entropy, dilaton charge, and magnetic potential, we show that the first law of black hole thermodynamics is satisfied by these quantities and the dilaton charge is not independent of mass and magnetic charge. Furthermore, for Bianchi type V, the T-dual black hole solution is obtained which carries no charge associated with B-field and the entropy turns to be invariant under the T-duality.

Thermodynamics of logarithmic charged black holes in the Einstein-dilaton gravity theory

Starting from the suitable action of four-dimensional Einstein-dilaton gravity with the logarithmic nonlinear electrodynamics, the explicit form of the coupled scalar, electromagnetic and gravitational field equations have been obtained. Through the exact solution of the field equations, the nonvanishing component of the electromagnetic tensor have been obtained and it has been shown that dilaton potential can be written as the suitable combination of two terms similar to the Liouville potentials. Three classes of novel electrically charged hairy black holes have been introduced with the regular and well-defined metric functions for all values of the parameters in the theory. The solutions reduce to their corresponding values in the Einstein-Maxwell-dilaton theory when the nonlinearity parameter of the electrodynamics goes to infinity. The thermodynamic quantities, such as temperature, entropy, mass, electric charge and electric potential, have been calculated and it has been demonstrated that the first law of black hole thermodynamics is valid for all of the new solutions. Thermodynamic stability or phase transition of the black holes have been investigated based on the canonical ensemble method. By calculating the black hole heat capacity type-1 and type-2 phase transition points have been determined. Also, it has been found that in order for the new nonlinearly charged dilaton black holes to remain locally stable some simple conditions must be fulfilled.

Effect of the hair on deflection angle by asymptotically flat black holes in Einstein-Maxwell-dilaton theory

In this paper, we are interested in a model of exact asymptotically flat charged hairy black holes in the background of dilaton potential. We study the weak gravitational lensing in the spacetime of hairy black hole in Einstein-Maxwell theory with a non-minimally coupled dilaton and its non-trivial potential. In doing so, we use the optical geometry of the flat charged hairy black hole for some range of parameter $\gamma$. For this purpose, by using Gauss-Bonnet theorem, we obtain the deflection angle of photon in a spherically symmetric and asymptotically flat spacetime. Moreover, we also investigate the impact of plasma medium on weak gravitational lensing by asymptotically flat charged hairy black hole with a dilaton potential. Our analytically analyses show the effect of the hair on the deflection angle in weak field limits.

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.

Entropy of the electrically charged hairy black holes

In this paper, we discuss the effective thermodynamic quantities of higher dimensional electrically charged hairy black holes in de Sitter spacetime, considering the correlation between the black hole horizon and the cosmological horizon. Our results show that, the interaction term determined by the position of the two horizons could significantly contribute to the total entropy of de Sitter spacetime. Moreover, different from the case in AdS spacetime, we find both zero-order and second-order phase transitions under certain conditions, with the absence of first-order phase transition in the electrically charged hairy black holes. These results are strongly supported by the classification of phase transition in Ehrenfest’s equations. More interestingly, our analysis demonstrates the validity of the Ehrenfest equations at the critical point, and futhermore indicates the similarity of Prigogine–Defay (PD) ratio between ECBH spacetime and AdS spacetime.

Extremal black holes, Stueckelberg scalars and phase transitions

We calculate the entropy of a static extremal black hole in 4D gravity, non-linearly coupled to a massive Stueckelberg scalar. We find that the scalar field does not allow the black hole to be magnetically charged. We also show that the system can exhibit a phase transition due to electric charge variations. For spherical and hyperbolic horizons, the critical point exists only in presence of a cosmological constant, and if the scalar is massive and non-linearly coupled to electromagnetic field. On one side of the critical point, two extremal solutions coexist: Reissner-Nordström (A)dS black hole and the charged hairy (A)dS black hole, while on the other side of the critical point the black hole does not have hair. A near-critical analysis reveals that the hairy black hole has larger entropy, thus giving rise to a zero temperature phase transition. This is characterized by a discontinuous second derivative of the entropy with respect to the electric charge at the critical point. The results obtained here are analytical and based on the entropy function formalism and the second law of thermodynamics.

Holographic Van der Waals phase transition of the higher-dimensional electrically charged hairy black hole

With motivation by holography, employing black hole entropy, two-point connection function and entanglement entropy, we show that, for the higher-dimensional Anti-de Sitter charged hairy black hole in the fixed charged ensemble, a Van der Waals-like phase transition can be observed. Furthermore, based on the Maxwell equal-area construction, we check numerically the equal-area law for a first order phase transition in order to further characterize the Van der Waals-like phase transition.

Superradiant instability of near extremal and extremal four-dimensional charged hairy black holes in anti–de Sitter spacetime

We study the instability of near extremal and extremal four-dimensional AdS charged hairy black hole to radial neutral massive and charged massless scalar field perturbations. We solve the scalar field equation by using the improved asymptotic iteration method and the time domain analysis and we find the quasinormal frequencies. For the charged scalar perturbations, we find the superradiance condition by computing the reflection coefficient in the low-frequency limit and we show that in the superradiance regime, which depends on the scalar hair charge, all modes of radial charged massless perturbations are unstable, indicating that the charged hairy black hole is superradiantly unstable. On the other hand, calculating the quasinormal frequencies of radial neutral scalar perturbations in this background, we found stability of the charged hairy black hole.

Four-dimensional black holes with scalar hair in nonlinear electrodynamics

We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and a U(1) nonlinear electromagnetic field. Solving analytically and numerically the coupled system for both power-law and Born-Infeld type electrodynamics, we find charged hairy black hole solutions. Then, we study the thermodynamics of these solutions and we find that at a low temperature the topological charged black hole with scalar hair is thermodynamically preferred, whereas the topological charged black hole without scalar hair is thermodynamically preferred at a high temperature for power-law electrodynamics. Interestingly enough, these phase transitions occur at a fixed critical temperature and do not depend on the exponent $p$ of the nonlinearity electrodynamics.