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 disentangle the mode-mixings into canonical normal modes, but the reduced metrics for these normal modes are mode-dependent. Despite of this, the resultant Hawking flux turns out to be mode-independent and remains the same as the Schwarzschild's one. Thus, one cannot tell the black holes with nonlinear supertranslation hairs from the Schwarzschild's one by examining the Hawking flux, so that the nonlinear soft hairs can be thought as the microstates.
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…
The Rindler horizon in Minkowski spacetime can be implanted with supertranslation hair by a matter shock wave without planar symmetry, and the hair is observable as a supertranslation memory on the Rindler family of uniformly linearly accelerated observers. We show that this classical memory is accompanied by a supertranslation quantum memory that modulates the entanglement between the opposing Rindler wedges in quantum field theory. A corresponding phenomenon across a black hole horizon may play a role in Hawking, Perry and Strominger's proposal for supertranslations to provide a solution to …
It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass $M$, momentum $\vec P$, angular momentum $\vec J$ and boost charge $\vec K$, an infinite head of supertranslation hair. The distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with supertranslation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in a…
Matter fields are supertranslated upon crossing a shock wave, which leads to entanglement of the quantum vacuum between the two regions on either side of the shock wave. We probe this entanglement for a scalar field in a planar shock wave background by computing the Bogoliubov transformation between the inertial and uniformly accelerated observer. The resulting Bogoliubov coefficients are shown to reproduce the standard Unruh effect without dependence on the form factor of the shock wave. In contrast, excited states lead to observables that depend upon the form factor. In the context of nonsph…
We discuss BMS supertranslations both at null-infinity and on the horizon for the case of the Schwarzschild black hole. We show that both kinds of supertranslations lead to infinetly many gapless physical excitations. On this basis we construct a quotient algebra using suited superpositions of both kinds of transformations which cannot be compensated by an ordinary BMS-supertranslation and therefore are intrinsically due to the presence of an event horizon. We show that these quotient transformations are physical and generate gapless excitations on the horizon that can account for the gravitat…
In a black hole, hair and quantum information retrieval are interrelated phenomena. The existence of any new form of hair necessarily implies the existence of features in the quantum-mechanically evaporated radiation. Classical supertranslation hair can be only distinguished from global diffeomorphisms if we have access to the interior of the black hole. Indirect information on the interior can only be obtained from the features of the quantum evaporation. Supertranslations $(T^-,T^+) \in BMS_{-}\otimes BMS_{+}$ can be used as bookkepers of the probability distributions of the emitted quanta w…
We study the boundary CFT under supertranslation in terms of the AdS/CFT correspondence. In particular, we probe the soft hair BTZ background by several open string configurations as follows. The Ryu-Takayanaki formula of holographic entanglement remains intact under supertranslation. The U-shape string probe indicates that the flat part of meson potential is altered by the soft charge. The trailing string solution shows that the hair parameter plays the role of external field in the drag force. The study of hanging string in the Brownian motion suggests the transport variables, such as fricti…
Degrees of freedom that carry black hole entropy and hair can be described in the language of Goldstone phenomenon. They represent the pseudo-Goldstone bosons of certain supertranslations, called A-transformations, that are spontaneously broken by the black hole metric. This breaking gives rise to a tower of Goldstone bosons created by the spontaneously-broken generators that can be labeled by spherical harmonics. Classically, the number of charges is infinite, they have vanishing VEVs and the corresponding Goldstone modes are gapless. The resulting hair and entropy are infinite, but unresolva…
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.
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…
Using the analytical solution for the Schwarzschild metric containing supertranslation field, we consider two main ingredients of calculation of the thermal Hawking black hole radiation: solution for eigenmodes of the d'Alambertian and solution of the geodesic equations for null geodesics. For calculation of Hawking radiation it is essential to determine the behavior of both the eigenmodes and geodesics in the vicinity of horizon. The equation for the eigenmodes is solved, first, perturbatively in the ratio $O(C)/M$ of the supertranslation field to the mass of black hole, and, next, non-pertur…
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 …
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.
It has recently been shown that BMS supertranslation symmetries imply an infinite number of conservation laws for all gravitational theories in asymptotically Minkowskian spacetimes. These laws require black holes to carry a large amount of soft ($i.e.$ zero-energy) supertranslation hair. The presence of a Maxwell field similarly implies soft electric hair. This paper gives an explicit description of soft hair in terms of soft gravitons or photons on the black hole horizon, and shows that complete information about their quantum state is stored on a holographic plate at the future boundary of …
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…
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.
We attempt to address the question of whether standard tests of general relativity can detect the presence of a black hole carrying a supertranslation field. In this regard, we study the photon sphere of a dynamical black hole carrying a supertranslation hair. We find that the dynamics of the photon sphere is quite subtle and it may offer an opportunity to differentiate a supertranslated black hole from its bald counterpart. This represents a first step towards understanding the observational signatures of a supertranslated dynamical black hole.
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.
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…
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…
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.
In a Rindler-type coordinate system spanned in a region outside of a black hole horizon, we have nonvanishing classical holographic charges as soft hairs on the horizon for stationary black holes. Taking a large black hole mass limit, the spacetimes with the charges are described by asymptotic Rindler metrics. We construct a general theory of gravitational holographic charges for a (1+3)-dimensional linearized gravity field in the Minkowski background with Rindler horizons. Although matter crossing a Rindler horizon causes horizon deformation and a time-dependent coordinate shift, that is, gra…
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 revisit the theory of null shells in general relativity, with a particular emphasis on null shells placed at horizons of black holes. We study in detail the considerable freedom that is available in the case that one solders two metrics together across null hypersurfaces (such as Killing horizons) for which the induced metric is invariant under translations along the null generators. In this case the group of soldering transformations turns out to be infinite dimensional, and these solderings create non-trivial horizon shells containing both massless matter and impulsive gravitational wave …
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 …
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-…
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.
Light bending by the strong gravity around the black hole will form the so-called black hole shadow, the shape of which can shed light on the structure of the near-horizon geometry to possibly reveal novel physics of strong gravity and black hole. In this work, we adopt both analytical and ray-tracing methods to study the black hole shadow in the presence of the infrared structure of gravity theory, which manifests the asymptotic symmetries of spacetime as the supertranslation soft hairs of the black hole. Though the black hole metrics with and without the soft hair are related by large gauge …
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 supertranslated black hole proposed by Hawking, Perry, and Strominger might provide a resolution to the information paradox, which is usually defined by a complicated space-time metric with even less space-time symmetries compared to Kerr black hole. In this paper, we figure out the shadow for the supertranslated Schwarzschild black hole by making use of supertranslated 4-velocities and the trajectories of the light rays. Based on this approach, we find that the photon sphere gets distorted due to the supertranslation hairs and the position of the shadow on the projection plane is shifted …
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.
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.
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 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…
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 …
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 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…
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…
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.
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 …
