For Hawking radiation, treated as a tunneling process, the no-hair theorem of black hole together with the law of energy conservation is utilized to postulate that the tunneling rate only depends on the external qualities (e.g., the mass for the Schwarzschild black hole) and the energy of the radiated particle. This postulate is justified by the WKB approximation for calculating the tunneling probability. Based on this postulate, a general formula for the tunneling probability is derived without referring to the concrete form of black hole metric. This formula implies an intrinsic correlation between the successive processes of the black hole radiation of two or more particles. It also suggests a kind of entropy conservation and thus resolves the puzzle of black hole information loss in some sense.
In this paper, we considered new solutions for four-dimensional asymptotically AdS black holes with scalar hair and discuss about Hawking temperature in the context of dark energy by using the tunneling method. We obtain modification of the Hawking temperature due to presence of the dark energy.
We study the Hawking radiation of 3D rotating hairy black holes. More concretely, we compute the transition probability of a bosonic and fermionic particle in such backgrounds. Thew, we show that the transition probability is independent of the nature of the particle. It is observed that the charge of the scalar hair B and the rotation parameter a control such a probability.
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…
In this paper, we study the Hawking radiation of Dirac particles via tunneling formalism from linearly supertranslated Schwarzschild black hole. We find that the radiation spectrum and the Hawking temperature remain the same as the one without soft hair. We extend the same analysis to the linearly supertranslated Vaidya black hole and find that particles can not tunnel through the horizon from the inside. We further comment on the validity of tunneling formalism in the study of Hawking radiation of dynamical black hole.
We study the Hawking flux from a black hole with soft hair by the anomaly cancellation method proposed by Robinson and Wilczek. Unlike the earlier studies considering the black hole with linear supertranslation hair, our study takes into account the supertranslation hair to the quadratic order, which then yields the angular dependent horizon. As a result, highly nontrivial kinetic-mixings appear among the spherical Kaluza-Klein modes of the (1+1)d near-horizon reduced theory, which obscures the traditional derivation of the Hawking flux. However, after a series of field re-definitions, we can …
We propose a model with multiple qubits that reproduces the thermal properties of 4-dimensional (4-dim) Schwarzschild black holes (BHs) by simultaneously taking account of the emission of Hawking particles and the zero-energy soft hair evaporation at horizon. The results verify that the entanglement entropy between a qubit and other subsystems, including emitted radiation, is much larger than the BH entropy analogue of the qubit, as opposed to the Page curve prediction. Our result suggests that early Hawking radiation is entangled with soft hair, and that late Hawking radiation can be highly e…
We revisit the Parikh-Wilczek's tunneling model of Hawking radiation in the Schwarzschild black hole with soft hair. Unlike the no-hair black hole, tunneling through the degenerate event horizon generated by supertranslation hair picks up an angular dependence, which suggests a hairy modification to the Bekenstein-Hawking entropy. At last, we discuss several implications and possible observable of soft hair.
Hairy Kiselev black hole with quintessential matter: themodynamic properties, sparsity of Hawking radiation, and greybody factors
The Assam Royal Global University（阿萨姆皇家全球大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Secretaria da Educação do Ceará (SEDUC)（塞阿拉州教育厅）；Echahid Cheikh Larbi Tebessi University（谢赫·拉里比·特贝西大学）
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…
Recently a set of diffeomorphisms were found which act nontrivially on the Kerr horizon and form a left-right pair of Virasoro algebras. Using the boundary formula for the associated central charge and assuming applicability of the Cardy formula to a putative dual CFT, the Bekenstein-Hawking entropy for the Kerr black hole was reproduced. In this paper, the addition of charge to the black hole is shown to require a minimal modification to this construction which then reproduces the Bekenstein-Hawking entropy for the Kerr-Newman black hole.
One interesting proposal to solve the black hole information loss paradox without modifying either general relativity or quantum field theory, is the soft hair, a diffeomorphism charge that records the anisotropic radiation in the asymptotic region. This proposal, however, has been challenged, given that away from the source the soft hair behaves as a coordinate transformation that forms an Abelian group, thus unable to store any information. To maintain the spirit of the soft hair but circumvent these obstacles, we consider Hawking radiation as a probe sensitive to the entire history of the b…
We investigate the thermodynamics of a general class of exact 4-dimensional asymptotically Anti-de Sitter hairy black hole solutions and show that, for a fixed temperature, there are small and large hairy black holes similar to the Schwarzschild-AdS black hole. The large black holes have positive specific heat and so they can be in equilibrium with a thermal bath of radiation at the Hawking temperature. The relevant thermodynamic quantities are computed by using the Hamiltonian formalism and counterterm method. We explicitly show that there are first order phase transitions similar to the Hawk…
In the context of black hole chemistry, we study the thermodynamics of asymptotically de Sitter black holes with conformal scalar hair in Einstein gravity. The hair parameter allows us to attain thermodynamic equilibrium between the event horizon and the cosmological horizon. We find that the system of the black hole and the de Sitter space surrounding it undergo a Reverse Hawking-Page phase transition provided we consider the grand-canonical ensemble.
Using a combination of analytical and numerical methods, we obtain a two-dimensional spacetime describing a black hole with tachyon hair. The physical ADM mass of the black hole is finite. The presence of tachyon hair increases the Hawking temperature.
The present thesis attempts to study the effect of scalar fields on Hawking radiation and quasinormal modes of black holes. We selected a static, spherically symmetric electrically charged black hole with an additional scalar 'hair' for our analysis. The scalar 'hair' is sourced by a scalar field, conformally coupled to the Einstein-Hilbert action. The scalar field can survive even in the absence of the black hole's electric charge and is characterized as a 'primary hair'. This scalar field changes the gravitational constant, and hence modifies the ADM (Arnowitt-Deser-Missner) mass of the blac…
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 propose a model for the geometry of a dynamical spherical shell in which the metric is asymptotically Schwarzschild, but deviates from Ricci-flatness in a finite neighbourhood of the shell. Hence, the geometry corresponds to a `hairy' black hole, with the hair originating on the shell. The metric is regular for an infalling shell, but it bifurcates, leading to two disconnected Schwarzschild-like spacetime geometries. The shell is interpreted as either collapsing matter or as Hawking radiation, depending on whether or not the shell is infalling or outgoing. In this model, the Hawking radiati…
The conservation of energy implies that an isolated radiating black hole cannot have an emission spectrum that is precisely thermal. Moreover, the no-hair theorem is only approximately applicable. We consider the implications for the black hole information puzzle.
We study a family of four-dimensional, asymptotically flat, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly, the maximum charge for given mass is a nonsingular hairy black hole with nonzero Hawking temperature. The implications for Hawking evaporation are discussed.
The total number of Hawking quanta emitted during the evaporation of a Schwarzschild black hole is proportional to the square of the initial mass or, equivalently, to the Bekenstein entropy. This simple, but little appreciated, fact is interpreted in terms of the recent discovery of black hole soft hair.
We regard the Parikh-Wilczek's tunnelling model of Hawking radiation as a quantum mechanical process of stimulated emission. The hypothesized microstates are found at the horizon with double degeneracy. A Jaynes-Cummings toy model for a black hole in the cavity is proposed to demonstrate how to write a qubit via the angular-dependent transition coupling, which might be related to the soft Goldstone hairs at analytic continuation. At last, we show how information is retained in the black hole by computing the time evolution of mutual entanglement entropy in the cavity-black holes system.
It has long been known that matter charged under a broken U(1) gauge symmetry collapsing to form a black hole will radiate away the associated external (massive) gauge field. We show that the timescale for the radiation of the monopole component of the field will be on the order of the inverse Compton wavelength of the gauge boson (assuming natural units). Since the Compton wavelength for a massive gauge boson is directly related to the scale of symmetry breaking, the timescale for a black hole to lose its gauge field "hair" is determined only by this scale. The timescale for Hawking radiation…
Three-dimensional Einstein gravity with negative cosmological constant admits stationary black holes that are not necessarily spherically symmetric. We propose boundary conditions for the near horizon region of these black holes that lead to a surprisingly simple near horizon symmetry algebra consisting of two affine u(1) current algebras. The symmetry algebra is essentially equivalent to the Heisenberg algebra. The associated charges give a specific example of "soft hair" on the horizon, as defined by Hawking, Perry and Strominger. We show that soft hair does not contribute to the Bekenstein-…
In this invited review, we describe Hawking's information paradox and a recently proposed resolution of it. Explicit calculations demonstrate the existence of quantum hair on black holes, meaning that the quantum state of the external graviton field depends on the internal state of the black hole. Simple quantum mechanics then implies that Hawking radiation amplitudes depend on the internal state, resulting in a pure final radiation state that preserves unitarity and, importantly, violates a factorization assumption which is central to the original paradox. Black hole information is encoded in…
The Bekenstein-Hawking entropy for certain BPS-saturated black holes in string theory has recently been derived by counting internal black hole microstates at weak coupling. We argue that the black hole microstate can be measured by interference experiments even in the strong coupling region where there is clearly an event horizon. Extracting information which is naively behind the event horizon is possible due to the existence of statistical quantum hair carried by the black hole. This quantum hair arises from the arbitrarily large number of discrete gauge symmetries present in string theory.
A recent, intriguing paper by Hawking, Perry and Strominger suggests that soft photons and gravitons can be regarded as black hole hair and may be relevant to the black hole information paradox. In this note we make use of factorization theorems for infrared divergences of the S-matrix to argue that by appropriately dressing in and out hard states, the soft-quanta-dependent part of the S-matrix becomes essentially trivial. The information paradox can be fully formulated in terms of dressed hard states, which do not depend on soft quanta.
Classically, the black hole (BH) horizon is completely opaque, hiding any clues about the state and very existence of its interior. Quantum mechanically and in equilibrium, the situation is not much different: Hawking radiation will now be emitted, but it comes out at an extremely slow rate, is thermal to a high degree of accuracy and thus carries a minimal amount of information about the quantum state within the BH. Here, it is shown that the situation is significantly different when a quantum BH is out of equilibrium. We argue that the BH can then emit "supersized" Hawking radiation with a m…
The membrane paradigm posits that black hole microstates are dynamical degrees of freedom associated with a physical membrane vanishingly close to the black hole's event horizon. The soft hair paradigm postulates that black holes can be equipped with zero-energy charges associated with residual diffeomorphisms that label near horizon degrees of freedom. In this essay we argue that the latter paradigm implies the former. More specifically, we exploit suitable near horizon boundary conditions that lead to an algebra of `soft hair charges' containing infinite copies of the Heisenberg algebra, ass…
We demonstrate the existence of quantum hair in electrodynamics and gravity using effective action techniques. In the case of electrodynamics we use the Euler-Heisenberg effective action while in the case of quantum gravity we use the unique effective action. We give a general formulation of these effects which applies to both theories and discuss analogies and differences between them. Furthermore, we present a QED analog to black hole evaporation. Spontaneous pair production in the external field of a ball of charge is analogous to Hawking radiation from black holes. Assuming spherical symme…
We revisit Carlip's approach to entropy counting. This analysis reemerged in a recently obtained Schwarzschild/CFT-correspondence as Sugawara-construction of a 2D stress-tensor. Here, for the example of a Schwarzschild black hole, we show how to single out diffeomorphisms forming in contrast to Carlip's analysis the full 2D local conformal algebra. We provide arguments, why their Hamiltonian generators are expected to be the symmetry generators of a possible conformal field theory describing the part of phase space responsible for black hole microstates. Then, we can infer central charges and …
We build on the observation by Hawking, Perry and Strominger that a global black hole space-time supports a large number of soft hair degrees of freedom to shed new light on the firewall argument by Almheiri, Marolf, Polchinski, and Sully. We propose that the soft hair Goldstone mode is encoded in a classical transition function that connects the asymptotic and near horizon region. The entropy carried by the soft hair is part of the black hole entropy and encoded in the outside geometry. We argue that the infalling observer automatically measures the classical value of the soft mode before rea…
According to the standard view classically black holes carry no hair, whereas quantum hair is at best exponentially weak. We show that suppression of hair is an artifact of the semi-classical treatment and that in the quantum picture hair appears as an inverse mass-square effect. Such hair is predicted in the microscopic quantum description in which a black hole represents a self-sustained leaky Bose-condensate of N soft gravitons. In this picture the Hawking radiation is the quantum depletion of the condensate. Within this picture we show that quantum black hole physics is fully compatible wi…
Spherically symmetric magnetic and dyonic black holes with a magnetic charge $Q=2$ are studied in the Standard Model and general relativity. A magnetically charged black hole with mass below $9.3\times 10^{35}$ GeV has a "hairy" cloud of electroweak gauge and Higgs fields outside the event horizon with $1/m_W$ in size. An extremal magnetic black hole has a hair mass of 3.6 TeV, while an extremal dyonic black hole has an additional mass of $q^2 \times 1.6$ GeV for a small electric charge $q \ll 2π/e^2$. A hairy dyonic black hole with an integer charge is not stable and can decay into a magnetic…
We develop a unified framework for the construction of soft dressings at boundaries of spacetime, such as the null infinity of Minkowski spacetime and the horizon of a Schwarzschild black hole. The construction is based on an old proposal of Mandelstam for quantizing QED and considers matter fields dressed by Wilson lines. Along time-like paths, the Wilson lines puncturing the boundary are the analogs of flat space Faddeev-Kulish dressings. We focus on the Schwarzschild black hole where our framework provides a quantum-field-theoretical perspective of the Hawking-Perry-Strominger viewpoint tha…
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.
It is known that there is no three-dimensional analog of de Sitter black holes. I show that the analog does exist when non-Gaussian (i.e., ring-type) smearings of point matter hairs are considered. This provides a new way of constructing black hole solutions from hairs. I find that the obtained black hole solutions are quite different from the usual large black holes in that there are i) large to small black hole transitions which may be considered as inverse Hawking-Page transitions and ii) soliton-like (i.e., non-perturbative) behaviors. For Gaussian smearing, there is no black hole but a gr…
Three-dimensional black holes coupled to a self-interacting scalar field is considered. It is known that its statistical entropy $a' la$ Strominger does $not$ agree with the Bekenstein-Hawking (BH) entropy. However I show that, by a careful treatment of the vacuum state in the {\it canonical} ensemble with a fixed temperature, which is the same as that of the BTZ black hole without the scalar field, the BH entropy is exactly produced by the Cardy's formula. I discuss its several implications, including the fate of black holes, no-scalar-hair theorems, stability, mirror black holes, and one-loo…
Black hole complementarity, as originally formulated in the 1990's by Preskill, 't Hooft, and myself is now being challenged by the Almheiri-Marolf-Polchinski-Sully firewall argument. The AMPS argument relies on an implicit assumption---the ``proximity postulate---which says that the interior of a black hole must be constructed from degrees of freedom that are physically near the black hole. The proximity postulate manifestly contradicts the idea that interior information is redundant with information in Hawking radiation, which is very far from the black hole. AMPS argue that a violation of t…
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…
We demonstrate within the quantum field theoretical framework that an asymptotic particle falling into the black hole implants soft graviton hair on the horizon, conforming with the classical proposal of Hawking, Perry and Strominger. A key ingredient to this result is the construction of gravitational Wilson line dressings of an infalling scalar field, carrying a definite horizon supertranslation charge. It is shown that a typical Schwarzschild state is degenerate, and can be labeled by different soft supertranslation hairs parametrized for radial trajectories by the mass and energy of the in…
Introducing a new form of scalar potential $V(ϕ)$, we derive a proper form of the rotating black hole solution in three-dimensional Einstein gravity with nonminimally coupled scalar field and find that the first law of thermodynamics of this new rotating hairy black hole can be protected, where the scalar field parameter $B$ is constrained to relate to the black hole size. We also disclose the Hawking-Page phase transition between this rotating hairy black holes and the pure thermal radiation. Moreover, we study phase transitions between this rotating hairy black hole and rotating BTZ black ho…
A rotating hairy black hole solution is found in gravity minimally coupled to a self-interacting real scalar field in three spacetime dimensions. Then we discuss analytically the horizon structure and find an analogue of the famous Kerr bound in (2+1) dimensions because of the existence of black hole horizons. We present the asymptotic symmetries and find the same symmetry group (i.e. the conformal group) and central charge as in pure gravity. Based on the asymptotic behavior, the mass and angular momentum are presented by the Regge-Teitelboim approach. Other thermodynamic quantities are also …
In 1974 Steven Hawking showed that black holes emit thermal radiation, which eventually causes them to evaporate. The problem of the fate of information in this process is known as the "black hole information paradox". Two main types of resolution postulate either a fundamental loss of information in Nature -- hence the breakdown of quantum mechanics -- or some sort of new physics, e.g. quantum gravity, which guarantee the global preservation of unitarity. Here we explore the second possibility with the help of recent developments in continuous-variable quantum information. Concretely, we empl…
The black hole information paradox presumes that quantum field theory in curved spacetime can provide unitary propagation from a near-horizon mode to an asymptotic Hawking quantum. Instead of invoking conjectural quantum gravity effects to modify such an assumption, we propose a self-consistency check. We establish an analogy to Feynman's analysis of a double-slit experiment. Feynman showed that unitary propagation of the interfering particles, namely ignoring the entanglement with the double-slit, becomes an arbitrarily reliable assumption when the screen upon which the interference pattern i…
We present new planar dyonic black hole solutions of the ${\mathfrak {su}}(N)$ Einstein-Yang-Mills equations in asymptotically anti-de Sitter space-time, focussing on ${\mathfrak {su}}(2)$ and ${\mathfrak {su}}(3)$ gauge groups. The magnetic part of the gauge field forms a condensate close to the planar event horizon. We compare the free energy of a non-Abelian hairy black hole with that of an embedded Reissner-Nordström-anti-de Sitter (RN-AdS) black hole having the same Hawking temperature and electric charge. We find that the hairy black holes have lower free energy. We present evidence that…
We present analytical perturbative, and numerical solutions of the Einstein equation which describe a black hole with a nontrivial dilaton field and a purely topological gauge potential. The gauge potential has zero field strength and hence no stress-energy, but it does couple to virtual string worldsheets which wrap around the Euclidean horizon two-sphere, and generate an effective interaction in the spacetime lagrangian. We use the lagrangian with a nonstandard potential for a scalar field that reproduces the effect of the worldsheet instantons. As has been previously pointed out the topolog…
We provide the first explicit proposal for all microstates of generic black holes in three dimensions (of Banados-Teitelboim-Zanelli-type): black hole microstates, termed "horizon fluffs", are a particular class of near horizon soft hairs which have zero energy as measured by the horizon observer and cannot be distinguished by observers at finite distance from the horizon. These states are arranged in orbits of the two-dimensional conformal algebra associated with the asymptotic black hole geometry. We count these microstates using the Hardy-Ramanujan formula for the number of partitions of a …
