In this study, the gravitational decoupling approach via extended geometric deformation is utilized to generate analytical black hole solutions owing to its simplicity and effectiveness. Considering the external fields surrounding Schwarzschild AdS black holes, we derive hairy black hole solutions in asymptotic AdS spacetime, satisfying the strong and dominant energy conditions. Moreover, we find that if the black hole spacetime is a fluid system, the fluid under each of these conditions is anisotropic.
Regular hairy black holes through gravitational decoupling method
College of Physics Science and Technology, Hebei University（河北大学物理科学与技术学院）；Hebei Key Lab of Optic-Electronic Information and Materials, Hebei University（河北大学河北省光电信息材料重点实验室）；National-Local Joint Engineering Laboratory of New Energy Photoelectric Devices, Hebei University（河北大学新能源光电器件国家地方联合工程实验室）；Key Laboratory of High-pricision Computation and Application of Quantum Field Theory of Hebei Province, Hebei University（河北大学量子场论高精度计算与应用重点实验室）
Nonsingular hairy black holes by gravitational decoupling
College of Physics Science and Technology, Hebei University（河北大学物理科学与工程学院）；Hebei Key Lab of Optic-Electronic Information and Materials, Hebei University（河北大学河北省光电信息与材料重点实验室）；National-Local Joint Engineering Laboratory of New Energy Photoelectric Devices, Hebei University（河北大学新能源光电器件国家地方联合工程实验室）；Key Laboratory of High-pricision Computation and Application of Quantum Field Theory of Hebei Province, Hebei University（河北大学量子场论高精度计算与应用重点实验室）
Gravitational decoupling can add hair to the black holes by adding extra sources. The quasinormal modes of hairy black hole caused by gravitational decoupling for the massless scalar field, electromagnetic field, and gravitational perturbation are investigated. The equations of effective potential for three perturbations are derived in hairy black hole spacetime. We also study the time evolution corresponding to the three perturbations, and the quasinormal mode frequencies are calculated using the Prony method through the time-domain profiles. By analyzing the influence of the hairs ($α$, $l_0…
In this work we construct a static and spherically symmetric black hole geometry supported by a family of generic mono-parametric sources thorough the Gravitational Decoupling. The parameter characterizing the matter sector can be interpreted as hair which cannot be associated to any global charge. Although the solution is constructed by demanding the weak energy condition, we find that the resulting matter sector satisfies all the energy conditions at and outside the horizon. We study the effect of the hair on the periastron advance and the gravitational lensing of the black hole. We estimate…
Hairy black holes in the gravitational decoupling setup are studied from the perspective of conformal anomalies. Fluctuations of decoupled sources can be computed by measuring the way the trace anomaly-to-holographic Weyl anomaly ratio differs from unit. Therefore the gravitational decoupling parameter governing three hairy black hole metrics is then bounded to a range wherein one can reliably emulate AdS/CFT with gravitational decoupled solutions, in the tensor vacuum regime.
The gravitational decoupling method represents an extremely useful tool to obtain new solutions of the Einstein equations through minimal geometrical deformations. In this paper, we consider the hairy charged black hole obtained by the gravitational decoupling and calculate their Hawking temperature in order to compare it with the case when the hairs are ignored. We have found out that the hairs, under some conditions of black hole parameters, affect the Hawking temperature and can increase it. We have also found out that the black hole temperature, in hairy case, doesn't depend on the electri…
The behavior of hairy black hole solutions, obtained by the gravitational decoupling (GD) method, is investigated under scalar perturbations. The quasinormal mode frequencies of such solutions are regulated by GD hair. The numerically generated wave solutions are derived for a range of values for the GD hairy black hole parameters, with higher-frequency modes very sensitive to them. The results are confronted with the corresponding ones for the Schwarzschild solution, whose deviations from it demonstrate a unique physical identification of GD hairy black holes. The method here presented compri…
Black holes with hair represented by generic fields surrounding the central source of the vacuum Schwarzschild metric are examined under the minimal set of requirements consisting of i) the existence of a well defined event horizon and ii) the strong or dominant energy condition for the hair outside the horizon. We develop our analysis by means of the gravitational decoupling approach. We find that trivial deformations of the seed Schwarzschild vacuum preserve the energy conditions and provide a new mechanism to evade the no-hair theorem based on a primary hair associated with the charge gener…
Particle Dynamics and Thermodynamics of a Charged-Like Hairy Black Hole in Extended Gravitational Decoupling
Tongji University（同济大学）；The University of Lahore（拉合尔大学）；Khazar University（阿塞拜疆哈萨尔大学）；Jadara University（贾达拉大学）；Al-Hussein Bin Talal University（侯赛因·本·塔拉勒大学）；Escuela Superior Politécnica de Chimborazo (ESPOCH)（奇姆博拉索高等理工学院）
We study the method of extended gravitational decoupling in obtaining static black hole solutions satisfying Einstein's equations with a tensor vacuum. The source has quite generic characteristics and satisfies the strong energy condition. The stationary, axisymmetric counterpart of the static metric is obtained by applying the Newman-Janis and Azreg-Aïnou algorithms. The thermodynamics of the rotating solution is studied and the expressions of various thermodynamic quantities are derived. The dependence of the temperature, free energy and specific heat on the horizon radius is studied for var…
Echoes of a hairy black hole from gravitational decoupling
Guizhou University of Finance and Economics（贵州财经大学）；Eastern Mediterranean University（东地中海大学）；Universit degli Studi di Salerno（萨莱诺大学）；Istituto Nazionale di Fisica Nucleare - Gruppo Collegato di Salerno - Sezione di Napoli（意大利国家核物理研究所 - 萨莱诺协作组 - 那不勒斯分部）；Guizhou Minzu University（贵州民族大学）；Guizhou University（贵州大学）
We construct exact hairy AdS soliton solutions in Einstein-dilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate.
The horizon structure and thermodynamics of hairy spherically symmetric black holes generated by the gravitational decoupling method are carefully investigated. The temperature and heat capacity of the black hole is determined, as well as how the hairy parameters affect the thermodynamics. It allows the analysis of the thermal stability and the possible existence of a remanent black hole. We also calculate the Hawking radiation corrected by the generalized uncertainty principle. For such we consider the emission of fermions and apply the tunneling method to the generalized Dirac equation. It s…
By using the scaling symmetry in the reduced action formalism, we derive the novel Smarr relation which holds even for the hairy rotating AdS_3 black holes. And then, by using the Smarr relation we argue that the hairy rotating AdS_3 black holes are stable thermodynamically, compared to the non-hairy ones.
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 thermodynamic behavior of static and spherically symmetric hairy black holes in massive gravity. In this case, the black hole is surrounded in a spherical cavity with a fixed temperature on the surface. It is observed that these black holes have a phase transition similar to the liquid-gas phase transition of a Van der Waals fluid. Also, by treating the cosmological constant $Λ$ as a thermodynamic pressure $P$, we study the thermodynamic behavior of charged anti-de Sitter black holes in an ensemble with a pressure of $P$ and an electric potential $Φ$ as the natural variables. A se…
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 use numerical methods to exhaustively study a novel family of hairy black hole solutions in AdS$_5$. These solutions can be uplifted to solutions of type IIB supergravity with AdS$_5\times S^5$ asymptotics and are thus expected to play an important role in our understanding of AdS/CFT. We find an intricate phase diagram, with the aforementioned family of hairy black hole solutions branching from the Reissner-Nordström black hole at the onset of the superradiance instability. We analyse black holes with spherical and planar horizon topology and explain how they connect in the phase diagram. …
We investigate the thermodynamics of hairy black holes in asymptotically Anti-de Sitter (AdS) space, including backreaction. Resorting to the Euclidean path integral approach, we show that matter conformally coupled to Einstein gravity in five dimensions may exhibit a phase transition whose endpoint turns out to be a hairy black hole in AdS5 space. The scalar field configuration happens to be regular everywhere outside and on the horizon, and behaves asymptotically in such a way that respects the AdS boundary conditions that are relevant for AdS/CFT. The theory presents other peculiar features…
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 propose the modified version of the canonical energy which was introduced originally by Hollands and Wald. Our construction depends only on the Euler-Lagrange expression of the system and thus is independent of the ambiguity in the Lagrangian. After some comments on our construction, we briefly mention on the relevance of our construction to the boundary information metric in the context of the AdS/CFT correspondence. We also study the stability of three-dimensional hairy extremal black holes by using our construction.
We study separatively the quasinormal modes (QNM) of electromagnetic perturbations around three-dimensional anti-de Sitter(AdS) black holes in Jordan and Einstein frames, which are related by the conformal transformations and a redefinition of a scalar field. We find that, in the Jordan frame, the imaginary parts of QNM frequencies can reflect the thermodynamical stabilities of hairy black holes, including the possible phase transition between the hairy black hole and BTZ black hole, disclosed by examining the corresponding free energies. Similar results are also uncovered in the Einstein fram…
We study small charged black holes in global AdS spacetime in the presence of a charged massless minimally coupled scalar field. In a certain parameter range these black holes suffer from well known superradiant instabilities. We demonstrate that the end point of the resultant tachyon condensation process is a hairy black hole which we construct analytically in a perturbative expansion in the black hole radius. At leading order our solution is a small undeformed RNAdS black hole immersed into a charged scalar condensate that fills the AdS `box'. These hairy black hole solutions appear in a two…
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 AdS$_5\times$S$^5$ 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\righta…
Reeb-Wolf Improved Landauer Principle for Hairy Black Holes via Gravitational Decoupling
Facultad de Ciencias, Escuela Superior Politécnica de Chimborazo (ESPOCH)（奇姆博拉索高等理工学院）；Centro de Investigación y Desarrollo Científico Zétesis（泽特西斯科学研究与发展中心）；Department of Mathematics and Statistics, The University of Lahore（拉合尔大学数学与统计系）；Research Center of Astrophysics and Cosmology, Khazar University（哈萨尔大学天体物理学与宇宙学研究中心）；Jadara Research Center, Jadara University（贾达拉大学贾达拉研究中心）
We perturbatively construct a three-dimensional rotating AdS black hole with a real scalar hair. We choose the mass of a scalar field slightly above the Breitenlohner-Freedman bound and impose a more general boundary condition for the bulk scalar field at AdS infinity. We first show that rotating BTZ black holes are unstable against superradiant modes under our more general boundary condition. Next we construct a rotating hairy black hole perturbatively with respect to a small amplitude $ε$ of the scalar field, up to $O(ε^4)$. The lumps of non-linearly perturbed geometry admit only one Killing…
An exact hairy asymptotically locally AdS black hole solution with a flat horizon in the Einstein-nonlinear sigma model system in (3+1) dimensions is constructed. The ansatz for the nonlinear $SU(2)$ field is regular everywhere and depends explicitly on Killing coordinates, but in such a way that its energy-momentum tensor is compatible with a metric with Killing fields. The solution is characterized by a discrete parameter which has neither topological nor Noether charge associated with it and therefore represents a hair. A $U(1)$ gauge field interacting with Einstein gravity can also be incl…
After introducing the gravitational decoupling method and the hairy black hole recently derived from it, we investigate the formation of quantum hairy black holes by applying the horizon quantum mechanics formalism. It enables us to determine how external fields, characterized by hairy parameters, affect the probability of spherically symmetric black hole formation and the generalized uncertainty principle.
Motivated by the recent unified approach to the Smarr-like relation of AdS planar black holes in conjunction with the quasi-local formalism on conserved charges, we revisit the quantum statistical and thermodynamic relations of hairy AdS planar black holes. By extending the previous results, we identify the hairy contribution in the bulk and show that the holographic computation can be improved so that it is consistent with the bulk computation. We argue that the first law can be retained in its universal form while the relation between the on-shell renormalized Euclidean action and its free e…
The superradiant instability of Kerr-AdS black holes is studied by numerically solving the full 3+1 dimensional Einstein equations. We find that the superradiant instability results in a two stage process with distinct initial and secondary instabilities. At the end of the secondary instability the geometry oscillates at several distinct fundamental frequencies -- a multi-oscillating black hole. The multi-oscillating black hole is remarkably close to a black resonator, albeit with a bit of gravitational hair. During the hairy black resonator epoch, the evolution of the horizon area is consiste…
We consider the linear stability of $4$-dimensional hairy black holes with mixed boundary conditions in Anti-de Sitter spacetime. We focus on the mass of scalar fields around the maximally supersymmetric vacuum of the gauged $\mathcal{N}=8$ supergravity in four dimensions, $m^{2}=-2l^{-2}$. It is shown that the Schrödinger operator on the half-line, governing the $S^{2}$, $H^{2}$ or $\mathbb{R}^{2}$ invariant mode around the hairy black hole, allows for non-trivial self-adjoint extensions and each of them correspons to a class of mixed boundary conditions in the gravitational theory. Discardin…
We study condensation behaviors of static scalar fields in the regular asymptotically AdS reflecting star spacetime. With analytical methods, we provide upper bounds for the radii of the scalar hairy reflecting stars. Above the bound, there is no scalar hair theorem for the star. Below the bound, we numerically obtain charged scalar hairy reflecting star solutions and in particular, the radii of the hairy stars are discrete, which is similar to known results in other reflecting object backgrounds. For every set of parameters, we search for the largest AdS hairy star radius, study effects of pa…
We show that the no-hair theorem for scalar-tensor theories with bi-metric structure can be evaded. We find that hairy black hole solutions in the presence of an electric charge admit AdS, flat or dS asymptotics with spherical, flat, or hyperbolic base manifolds. Spherically symmetric, asymptotically flat black holes and asymptotically AdS configurations with any horizon topology are compatible with a regular scalar field on and outside the event horizon. The latter presents a rich thermodynamic behavior induced by the disformal factor that enters as a coupling parameter in the theory. In the …
In this work, we implement the $13^{th}$ order semi-analytical WKB method to explore the stability of hairy black holes obtained in the framework of Gravitational Decoupling. In particular, we perform a detailed analysis of the frequencies of the quasi-normal modes as a function of the primary hair of the solutions with the aim to bound their values. We explore a broad interval in a step of 0.1 of the hair parameters. We find that except for some cases where the method is expected to have poor accuracy, all the solutions seem to be stable and the role played by the primary hair is twofold: to …
In this paper, we study thermodynamics and phase structure of asymptotically AdS hairy and Reissner-Nordström-AdS (RNAdS) black holes in the extended phase space, where the cosmological constant is interpreted as a thermal pressure. The RNAdS and hairy black holes are black hole solutions of an Einstein-Maxwell-scalar (EMS) model with a non-minimal coupling between the scalar and electromagnetic fields. The Smarr relation, the first law of thermodynamics and the free energy are derived for black hole solutions in the EMS model. Moreover, the phase structure of the RNAdS and hairy black holes i…
We consider three-dimensional gravity based on torsion. Specifically, we consider an extension of the so-called Teleparallel Equivalent of General Relativity in the presence of a scalar field with a self-interacting potential, where the scalar field is non-minimally coupled with the torsion scalar. Then, we find asymptotically AdS hairy black hole solutions, which are characterized by a scalar field with a power-law behavior, being regular outside the event horizon and null at spatial infinity and by a self-interacting potential, which tends to an effective cosmological constant at spatial inf…
We present different Taub-NUT/Bolt-anti de Sitter (AdS) solutions in a shift-symmetric sector of Horndeski theory of gravity possessing nonminimal kinetic coupling of scalar fields to the Einstein tensor. In four dimensions, we find locally and asymptotically locally AdS solutions possessing nontrivial scalar field. In higher dimensions, analytical Taub-NUT/Bolt-AdS p-branes and solitons are obtained, supported by the existence of p Horndeski scalar fields with axionic profile. The thermodynamical properties are studied through Euclidean methods and it is found that the first law of thermodyna…
We investigate whether supertranslation symmetry may appear in a scenario that involves black holes in AdS space. The framework we consider is massive 3D gravity, which admits a rich black hole phase space, including stationary AdS black holes with softly decaying hair. We consider a set of asymptotic conditions that permits such decaying near the boundary, and which, in addition to the local conformal symmetry, is preserved by an extra local current. The corresponding algebra of diffeomorphisms consists of two copies of Virasoro algebra in semi-direct sum with an infinite-dimensional Abelian …
We study rotating global AdS solutions in five-dimensional Einstein gravity coupled to a multiplet complex scalar within a cohomogeneity-1 ansatz. The onset of the gravitational and scalar field superradiant instabilities of the Myers-Perry-AdS black hole mark bifurcation points to black resonators and hairy Myers-Perry-AdS black holes, respectively. These solutions are subject to the other (gravitational or scalar) instability, and result in hairy black resonators which contain both gravitational and scalar hair. The hairy black resonators have smooth zero-horizon limits that we call gravibos…
We construct a new class of charged, rotating hairy black holes in a consistent truncation of $\mathcal{N} = 8$ supergravity, which retains one charged scalar field and a U$(1)$ gauge field. These hairy solutions can be uplifted to solutions of type IIB supergravity with AdS$_5\times$S$^5$ asymptotics. We find rotating hairy black holes with finite entropy arbitrarily close to the supersymmetric bound - the resulting supersymmetric solution is a one-parameter extension of the Gutowski-Reall solution. These solutions have finite curvature invariants (including at extremality), but in the extrem…
In a recent paper (Phys. Dark Univ. {\bf 31}, 100744 (2021)) it has been obtained new static black hole solutions with primary hairs by the Gravitational Decoupling. In this work we either study the geodesic motion of massive and massless particles around those solutions and restrict the values of the primary hairs by observational data. In particular, we obtain the effective potential, the innermost stable circular orbits, the marginally bounded orbit, and the periastron advance for time--like geodesics. In order to restrict the values taken by the primary hairs we explore their relationship …
We consider Einstein gravity in general dimensions, coupled to a scalar field either minimally or non-minimally, together with a generic scalar potential. By making appropriate choices of the scalar potential, we obtain large classes of new scalar hairy black holes that are asymptotic to anti-de Sitter spacetimes in planar coordinates. For some classes of solutions, we can promote the scalar charge to be dependent on the advanced or retarded times in the Eddington-Finkelstein coordinates, and obtain exact dynamic solutions. In particular, one class of the collapse solutions describe the evolut…
In this paper we apply the gravitational decoupling method for dynamical systems in order to obtain a new type of solution which can describe a hairy dynamical black hole. We consider three cases of decoupling. The first one is the simplest and well-known when the mass function is the function only of space coordinate $r$. The second case is Vaidya spacetime case when the mass function depends on time $v$ . And the third case represents the generalization of these two cases: the mass function is the function of both $r$ and $v$. We also calculate the apparent horizon and singularity location f…
We do a systematic study of the phases of gravity coupled to an electromagnetic field and charged scalar in flat space, with box boundary conditions. The scalar-less box has previously been investigated by Braden, Brown, Whiting and York (and others) before AdS/CFT and we elaborate and extend their results in a language more familiar from holography. The phase diagram of the system is analogous to that of AdS black holes, but we emphasize the differences and explain their origin. Once the scalar is added, we show that the system admits both boson stars as well as hairy black holes as solutions…
We introduce a systematic and direct procedure to generate hairy rotating black holes by deforming a spherically symmetric seed solution. We develop our analysis in the context of the gravitational decoupling approach, without resorting to the Newman-Janis algorithm. As examples of possible applications, we investigate how the Kerr black hole solution is modified by a surrounding fluid with conserved energy-momentum tensor. We find non-trivial extensions of the Kerr and Kerr-Newman black holes with primary hair. We prove that a rotating and charged black hole can have the same horizon as Kerr'…
We calculate QNMs of the scalar hairy black hole in the AdS background using Horowitz-Hubeny method for the potential that is not known in analytical form. For some black hole parameters we found pure imaginary frequencies. Increasing of the scalar field mass does not cause the imaginary part to vanish, it reaches some minimum and then increases, thus in the case under consideration the infinitely long living modes (quasi-resonances) do not appear.
