We obtain an exact static solution to Einstein-Power-Maxwell (EPM) theory in $(2+1)$ dimensional AdS spacetime, in which the scalar field couples to gravity in a non-minimal way. After considering the scalar potential, a stable system leads to a constraint on the power parameter $k$ of Maxwell field. The solution contains a curvature singularity at the origin and is non-conformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Especially for the cases with $k>1$, the lower bound is negative, thus there exist scalar black holes with negative mass. The null geodesics in this spacetime are also discussed in detail. They are divided into five models, which are made up of the cases with the following geodesic motions: no-allowed motion, the circular motion, the elliptic motion and the unbounded spiral motion.
Treating Maxwell soft hair as a transition function that relates U(1) gauge fields living in the asymptotic region and near-horizon region, the U(1) gauge parameter $ϕ$ naturally becomes a good label of those Maxwell soft hair degrees of freedom. This interpretation also builds the connection between Maxwell soft hair and U(1) edge modes living in the intermediate region, which admits a well-defined effective action description. We study the statistical properties by Euclidean path integral, which concludes that the soft hair density of state increases with black hole temperature. Hawking radi…
We obtain a newly charged BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole solution from the Einstein-Weyl-Maxwell-conformal (conformally coupled) scalar theory with a positive Weyl coupling parameter $m^2_2$ numerically. This solution has a primary scalar hair, compared to a secondary scalar hair in the charged BBMB black hole solution. The limiting case of $m_2^2\to\infty$ leads to the series form of the charged BBMB black hole solution. However, for $m^2_2<0$, we could not obtain any asymptotically flat black hole solution with scalar hair.
We obtain scalar hairy black holes from Einstein-Maxwell-conformally coupled scalar (EMCS) theory with the scalar coupling parameter $α$ to the Maxwell term. In case of $α=0$, the $α=0$ EMCS theory provides constant (charged) scalar hairy black hole and charged BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole where the former is stable against full perturbations, while the latter remains unstable because it belongs to an extremal black hole. It is noted that for $α\not=0$, the unstable Reissner-Nordström black holes without scalar hair imply infinite branches of $n=0(α\ge 8.019),1(α\g…
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 $γ$. 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 investig…
Recently, a no inner (Cauchy) horizon theorem for static black holes with non-trivial scalar hairs has been proved in Einstein-Maxwell-scalar theories. In this paper, we extend the theorem to the static black holes in Einstein-Maxwell-Horndeski theories. We study the black hole interior geometry for some exact solutions and find that the spacetime has a (space-like) curvature singularity where the black hole mass gets an extremum and the Hawking temperature vanishes. We discuss further extensions of the theorem, including general Horndeski theories from disformal transformations.
The no-hair theorem by Mayo and Bekenstein states that there exists no non-extremal static and spherical charged black hole endowed with hair in the form of a charged scalar field with a self-interaction potential. In our recent work, we showed that the effect of a scalar mass term is important at an asymptotic infinity, which was omitted to prove the no-hair theorem. In this paper, we demonstrate that there actually exists static and spherical charged scalar hair, dubbed as Q-hair, around charged black holes, by taking into account the backreaction to the metric and gauge field. We also discu…
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 prefer…
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 pert…
The strong gravitational lensing for charged black holes with scalar hair in Einstein-Maxwell-Dilaton theory are studied. We find, with the increase of scalar hair, that the radius of the photon sphere, minimum impact parameter, angular image position and relative magnitude increase, while the deflection angle and angular image separation decrease. Our results can be reduced to those of the Schwarzschild black hole in two cases, one of them is that the scalar hair disappears, the other is that the coupling constants take particular values with arbitrary scalar hair.
We study standard Einstein-Maxwell theory minimally coupled to a complex valued and self-interacting scalar field. We demonstrate that new, previously unnoticed spherically symmetric, charged black hole solutions with scalar hair exist in this model for sufficiently large gravitational coupling and sufficiently small electromagnetic coupling. The novel scalar hair has the form of a spatially oscillating ''wave packet'' and back-reacts on the space-time such that both the Ricci and the Kretschmann scalar, respectively, possess qualitatively similar oscillations.
Recently, spontaneous scalarization of charged black holes has attracted a great deal of attention and motivated several studies of Einstein-Maxwell-scalar models. These studies have, however, only considered a massless and non-self-interacting scalar field. In this work a more realistic treatment of the problem is considered by studying the effects of scalar field mass and self-interacting terms on spontaneous scalarization in Einstein-Maxwell-scalar models, and on the string theory motivated dilatonic black hole. We assess the domains of existence of the black hole solutions, thermodynamic p…
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 …
A mechanism for circumventing the Mayo-Bekenstein no-hair theorem allows endowing four dimensional $(D=4)$ asymptotically flat, spherical, electro-vacuum black holes with a minimally coupled $U(1)$-gauged scalar field profile: $Q$-$hair$. The scalar field must be massive, self-interacting and obey a {\it resonance condition} at the threshold of (charged) superradiance. We establish generality for this mechanism by endowing three different types of static black objects with scalar hair, within a $D=5$ Einstein-Maxwell-gauged scalar field model: asymptotically flat black holes and black rings; a…
A static spherically symmetric black hole usually turns out to be either a Schwarzschild black hole or a Reissner-Nordström black hole. This result was summarised by Ruffini and Wheeler as the so-called no hair conjecture which states that for a spherically symmetric black hole only the information about mass ($M$) and electric charge ($e$) of the black hole is available for an external observer. In this work, we calculate the emission rate of charged particles from an asymptotically flat charged spherically symmetric black hole endowed with a scalar hair using a semi-classical tunneling forma…
We establish a no inner-horizon theorem for black holes with charged scalar hairs. Considering a general gravitational theory with a charged scalar field, we prove that there exists no inner Cauchy horizon for both spherical and planar black holes with non-trivial scalar hair. The hairy black holes approach to a spacelike singularity at late interior time. This result is independent of the form of scalar potentials as well as the asymptotic boundary of spacetimes. We prove that the geometry near the singularity takes a universal Kasner form when the kinetic term of the scalar hair dominates, w…
In these lectures the properties of magnetically charged black holes are described. In addition to the standard Reissner-Nördstrom solution, there are new types of static black holes that arise in theories containing electrically charged massive vector mesons. These latter solutions have nontrivial matter fields outside the horizon; i.e., they are black holes with hair. While the solutions carrying unit magnetic charge are spherically symmetric, those with more than two units of magnetic charge are not even axially symmetric. These thus provide the first example of time-independent black hole …
We studied, both analytically and numerically, an Abelian Higgs vortex in the spacetime of stationary axisymmetric black hole being the solution of the low-energy limit of the heterotic string theory, acted as hair on the black hole background. Taking into account the gravitational backreaction of the vortex we show that its influence is far more subtle than causing only a conical defect. As a consequence of its existence, we found that the ergosphere was shifted as well as event horizon angular velocity was affected by its presence. Numerical simulations reveal the strong dependence of the vo…
Is it possible the no-hair paradigm is violated when a black hole undergoes an instability? Employing massless charged scalar perturbations, we address this question within the context of conformally invariant Einstein-Maxwell theory for some allowed $d$-dimensional ($d=4n+4$ with conformal parameter $n=0,1,2,...$ ) topological small AdS black-holes. We provide numerical analyses that show the non trivial scalar hairy black hole solutions to include planar and spherical horizon topologies in higher dimensions with an even conformal parameter $n$. It is also shown that the solutions presented h…
The `no-hair' conjecture claims that for a spherically symmetric black hole, only the information regarding the mass and charge of the black hole is available to an external observer. However, there are numerous counterexamples to the `no-hair' conjecture. In this work, we consider a particular counter-example to the `no-hair' conjecture in (3+1) dimensions, namely, a static spherically symmetric charged black hole with a scalar hair. We provide semi-analytic bounds on the greybody factors and study the sparsity of Hawking radiation of mass-less uncharged scalar fields. Our results show that t…
It is argued that an electronically charged dilaton black hole can support a long range field of a Nielsen-Olesen string. Combining both numerical and perturbative techniques we examine the properties of an Abelian-Higgs vortex in the presence of the black hole under consideration. Allowing the black hole to approach extremality we found that all fields of the vortex are expelled from the extreme black hole. In the thin string limit we obtained the metric of a conical electrically charged dilaton black hole. The effect of the vortex can be measured from infinity justifying its characterization…
We construct hairy black hole solutions that merge with the anti-de Sitter (AdS$_4$) Reissner-Nordström black hole at the onset of superradiance. These hairy black holes have, for a given mass and charge, higher entropy than the corresponding AdS$_4$-Reissner-Nordström black hole. Therefore, they are natural candidates for the endpoint of the charged superradiant instability. On the other hand, hairy black holes never dominate the canonical and grand-canonical ensembles. The zero-horizon radius of the hairy black holes is a soliton (i.e. a boson star under a gauge transformation). We construct…
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…
We study the stability of (4+1)-dimensional charged Gauss-Bonnet black holes and solitons. We observe an instability related to the condensation of a scalar field and construct explicit "hairy" black hole and soliton solutions of the full system of coupled field equations. We investigate the cases of a massless scalar field as well as that of a tachyonic scalar field. The solitons with scalar hair exist for a particular range of the charge and the gauge coupling. This range is such that for intermediate values of the gauge coupling a "forbidden band" of charges for the hairy solitons exists. W…
The recently proved `no short hair' theorem asserts that, if a spherically-symmetric static black hole has hair, then this hair (the external fields) must extend beyond the null circular geodesic (the "photonsphere") of the corresponding black-hole spacetime: $r_{\text{field}}>r_{\text{null}}$. In this paper we provide compelling evidence that the bound can be {\it violated} by {\it non}-spherically symmetric hairy black-hole configurations. To that end, we analytically explore the physical properties of cloudy Kerr-Newman black-hole spacetimes -- charged rotating black holes which support lin…
Can a black hole that suffers a superradiant instability evolve towards a 'hairy' configuration which is stable? We address this question in the context of Einstein-charged scalar field theory. First, we describe a family of static black hole solutions which possess charged scalar-field hair confined within a mirror-like boundary. Next, we derive a set of equations which govern the linear, spherically symmetric perturbations of these hairy solutions. We present numerical evidence which suggests that, unlike the vacuum solutions, the (single-node) hairy solutions are stable under linear perturb…
We analyze condensation behaviors of neutral scalar fields outside horizonless reflecting stars in the Einstein-Maxwell-scalar gravity. It was known that minimally coupled neutral scalar fields cannot exist outside horizonless reflecting stars. In this work, we consider non-minimal couplings between scalar fields and Maxwell fields, which is included to aim to trigger formations of scalar hairs. We analytically demonstrate that there is no hair theorem for small coupling parameters below a bound. For large coupling parameters above the bound, we numerically obtain regular scalar hairy configur…
The time-like and null-like geodesics around compact objects are some of the best tools to classify and understand the structure of a space-time. In this paper, we study the null geodesics around charged static dilaton black holes in Einstein-Maxwell-dilaton gravity. The physical parameters for non-radial geodesics including the effective potential, effective force, radius of the photon sphere and impact parameter are obtained and effects of the charge parameter and dilaton coupling constant on these quantities are studied. Possible photon motions for different values of the impact parameter a…
In Einstein-Maxwell theory black holes are uniquely determined by their mass, their charge and their angular momentum. This is no longer true in Einstein-Yang-Mills theory. We discuss sequences of neutral and charged SU(N) Einstein-Yang-Mills black holes, which are static spherically symmetric and asymptotically flat, and which carry Yang-Mills hair. Furthermore, in Einstein-Maxwell theory static black holes are spherically symmetric. We demonstrate that, in contrast, SU(2) Einstein-Yang-Mills theory possesses a sequence of black holes, which are static and only axially symmetric.
We study the phenomena of superradiance for $F(R)$-Maxwell black holes in an AdS space-time. The AdS boundary plays the role of a mirror and provides a natural confining system that makes the superradiant waves bouncing back and forth between the region near the horizon and the reflective boundary, causing a possible superradiant instability. We obtain numerical solutions for static hairy black holes in this scenario and investigate their instability and explicitly address the stability of such solutions for spherical perturbations under specific conditions for the scalar charge and AdS radius…
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 …
A new class of four-dimensional, hairy, stationary solutions of the Einstein-Maxwell-Lambda system with a conformally coupled scalar field is constructed in this paper. The metric belongs to the Plebanski-Demianski family and hence its static limit has the form of the charged C-metric. It is shown that, in the static case, a new family of hairy black holes arises. They turn out to be cohomogeneity-two, with horizons that are neither Einstein nor homogenous manifolds. The conical singularities in the C-metric can be removed due to the back reaction of the scalar field providing a new kind of re…
In this paper, we consider the Klein-Gordon equation in a 3D charged rotating hairy black hole background to study behavior of a massive scalar field. In the general case we find periodic-like behavior for the scalar field which may be vanishes at the black hole horizon or far from the black hole horizon. For the special cases of non-rotating or near horizon approximation we find radial solution of Klein-Gordon equation in terms of hypergeometric and Kummer functions. Also for the case of uncharged black hole we find numerical solution of the Klein-Gordon equation as periodic function which ma…
Behaviour of Dirac fermions in the background of a charged black string penetrated by an Abelian Higgs vortex is elaborated. One finds the evidence that the system under consideration can support fermion fields acting like a superconducting cosmic string in the sence that a nontrivial Dirac fermion field can be carried by the system in question. The case of nonextremal and extremal black string vortex systems were considered. The influence of electric and Higgs charge, the winding number and the fermion mass on the fermion localization near the black string event horizon was studied. It turned…
We study the system constructed by charged scalar fields linearly coupled to asymptotically flat horizonless compact reflecting stars. We obtain bounds on the charge of the scalar field, below which the scalar hairy star is expected to suffer from nonlinear instabilities. It means that scalar hairy regular configurations are unstable for scalar fields of small charge. For the highly-charged star, there are also bounds on radii of regular compact reflecting stars. When the star radius is below the bound, the hairy star is always unstable.
We study mass bounds of Maxwell fields in RN black holes and genuine hair in Einstein-Born-Infeld black holes with various cosmological constants. It shows that the Maxwell field serves as a good probe to disclose the hair distribution described with the event horizon and the photonsphere. And we find that the Hod's lower bound obtained in asymptotically flat space also holds in the asymptotically dS Einstein-Born-Infeld hairy black holes. In contrast, the Hod's lower bound can be invaded in the asymptotically AdS Einstein-Born-Infeld hairy black holes. It implies that the AdS boundary could m…
An electrically charged black hole solution with scalar hair in four dimensions is presented. The self-interacting scalar field is real and it is minimally coupled to gravity and electromagnetism. The event horizon is a surface of negative constant curvature and the asymptotic region is locally an AdS spacetime. The asymptotic fall-off of the fields is slower than the standard one. The scalar field is regular everywhere except at the origin, and is supported by the presence of electric charge which is bounded from above by the AdS radius. In turn, the presence of the real scalar field smooths …
We prove three theorems in general relativity which rule out classical scalar hair of static, spherically symmetric, possibly electrically charged black holes. We first generalize Bekenstein's no--hair theorem for a multiplet of minimally coupled real scalar fields with not necessarily quadratic action to the case of a charged black hole. We then use a conformal map of the geometry to convert the problem of a charged (or neutral) black hole with hair in the form of a neutral self--interacting scalar field nonminimally coupled to gravity to the preceding problem, thus establishing a no--hair th…
In this paper we construct rotating charged hairy black hole in (2+1) dimensions for infinitesimal black hole charge and rotation parameters. Then we consider this black hole as particle accelerator and calculate the center-of-mass energy of two colliding test particles near the rotating charged hairy black hole in (2+1) dimensions. As we expected, the center-of-mass energy has infinite value.
Einstein-Gauss-Bonnet-gravity (EGB) coupled minimally to a $U(1)$ gauged, massive scalar field possesses -- for appropriate choices of the $U(1)$ charge -- black hole solutions that carry charged scalar hair if the frequency of the harmonic time-dependence of the scalar field is equal to the upper bound on the superradiant frequency. The existence of these solutions has first been discussed in \cite{Grandi:2017zgz}. In this paper, we demonstrate that the critical value of the scalar charge results from the requirement of non-extremality of the charged black hole solutions and the fact that the…
We find the phase diagram of solutions of the charged black hole bomb system. In particular, we find the static hairy black holes of Einstein-Maxwell-Scalar theory confined in a Minkowski box. We impose boundary conditions such that the scalar field vanishes at and outside a cavity of constant radius. These hairy black holes are asymptotically flat with a scalar condensate floating above the horizon. We identify four critical scalar charges which mark significant changes in the qualitative features of the phase diagram. When they coexist, hairy black holes always have higher entropy than the R…
We construct charged soliton solutions around spherical charged black holes with no angular momentum in asymptotically flat spacetime. These solutions are non-linear generalizations of charged scalar clouds, dubbed Q-ball hair or Q-clouds, and they do not contradict the non-existence theorem for free (linear) scalar clouds around charged black holes. These solutions are the first examples of O(3) solutions for Q-clouds around a non-extremal and non-rotating BH in the Abelian gauge theory. We show that a solution exists with an infinitely short hair in the limit of extremal black holes. We disc…
In this paper, we consider the first order correction of the entropy and temperature in a charged black hole with a scalar field. Here, we apply such correction for the different cases of black holes. These corrections are due to the thermal fluctuations of statistical physics. Also, we take advantage of such corrections and study the $ P - V $ critically and phase transition. Also, we investigate the effect of correction on the critical point and stability of the system. We obtain modified thermodynamics quantities and find effects of thermal fluctuations in the stability of the black hole. W…
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 g…
We study the extended phase space thermodynamics for hairy AdS black hole solutions to Einstein-Maxwell-$Λ$ theory conformally coupled to a scalar field in five dimensions. We find these solutions to exhibit van der Waals behaviour in both the charged/uncharged cases, and reentrant phase transitions in the charged case. This is the first example of reentrant phase transitions in a five dimensional gravitational system which does not include higher curvature corrections.
We study scalar condensation in the background of asymptotically flat spherically symmetric regular Dirichlet stars. We assume that the scalar field decreases as the star surface is approached. Under these circumstances, we prove a no hair theorem for neutral regular compact stars. We also extend the discussion to charged regular compact stars and find an upper bound for the charged star radius. Above the upper bound, the scalar hair cannot exist. Below the upper bound, we numerically obtain solutions of scalar hairy charged stars.
We study the problem of vortex solutions in the background of rotating black holes in both asymptotically flat and asymptoticlly anti de Sitter spacetimes. We demonstrate the Abelian Higgs field equations in the background of four dimensional Kerr, Kerr-AdS and Reissner-Nordstrom-AdS black holes have vortex line solutions. These solutions, which have axial symmetry, are generalization of the Nielsen-Olesen string. By numerically solving the field equations in each case, we find that these black holes can support an Abelian Higgs field as hair. This situation holds even in the extremal case, an…
