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 the scalar and electric charges contribute oppositely to the greybody factor and the sparsity of the Hawking radiation cascade. Also, the greybody factor decreases and the Hawking emission spectra become more sparse with the reduction in the black hole (ADM) mass.
The greybody factor and the Hawking temperature for a class of asymptotically flat charged dilatonic black holes are computed by using the low-energy dynamics of scalar fields in the black hole background. In the semi-classical approximation, the Hawking temperature has a good agreement with the one computed from the surface gravity, which is independent of the magnetic (or electric) charges of dilatonic black holes.
We investigate Hawking radiation in the novel $4D$ Einstein-Gauss-Bonnet gravity which is recently formulated by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)]. We first find the constraints on $α$ and $Λ$ to retain a dS black hole in the spacetime. Both the greybody factor and the power spectra of the Hawking radiation of the massless scalar are studied for the full range of various parameters including the GB coupling constant $α$, the cosmological constant $Λ$ and the constant related to the scalar $ξ$ numerically. In particular, we find the greybody factor is larger for a negative $α…
We study the greybody factor and Hawking radiation for a scalar field coupling to Einstein's tensor in the background of Reissner-Nordström black hole in the low-energy approximation. We find that the presence of the coupling terms modifies the standard results in the greybody factor and Hawking radiation. Our results show that both the absorption probability and Hawking radiation increase with the coupling constant. Moreover, we also find that for the stronger coupling, the charge of black hole enhances the absorption probability and Hawking radiation of the scalar field, which is different f…
Gravitational decoupling can add hair to the black holes by adding extra sources. The quasinormal modes of hairy black hole caused by gravitational decoupling for the massless scalar field, electromagnetic field, and gravitational perturbation are investigated. The equations of effective potential for three perturbations are derived in hairy black hole spacetime. We also study the time evolution corresponding to the three perturbations, and the quasinormal mode frequencies are calculated using the Prony method through the time-domain profiles. By analyzing the influence of the hairs ($α$, $l_0…
Perturbations of black holes with primary hair: time evolutions, quasinormal modes and greybody factors
CEICO, Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；CENTRA, Departamento de Física, Instituto Superior Técnico - IST, Universidade de Lisboa - UL（里斯本大学技术学院物理系CENTRA）
We study the greybody factor and power spectra of Hawking radiation for the minimally or nonminimally coupled scalar field with exact numerical method in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black hole spacetime. The effects of scalar coupling constant, angular momentum number of scalar, spacetime dimension, cosmological constant and Gauss-Bonnet coupling constant on the Hawking radiation are studied in detail. Specifically, the Gauss-Bonnet coupling constant always increases the greybody factor in the entire energy regime. Different from the case of Schwarzschild-de Sitter bl…
In this work, we have considered a $n-$dimensional Schwarzschild-Tangherlini black hole spacetime with massless minimally coupled free scalar fields in its bulk and $3-$brane. The bulk scalar field equation is separable using the higher dimensional spherical harmonics on $(n-2)-$sphere. First, using the Hamiltonian formulation with the help of the recently introduced near-null coordinates we have obtained the expected temperature of the Hawking effect, identical for both bulk and brane localized scalar fields. Second, it is known that the spectrum of the Hawking effect as seen at asymptotic fu…
Charged massive scalar fields are studied in the gravitational, electromagnetic, dilaton, and axion fields of rotating linear dilaton black holes. In this geometry, we separate the covariant Klein-Gordon equation into radial and angular parts and obtain the exact solutions of both the equations in terms of the confluent Heun functions. Using the radial solution, we study the problems of resonant frequencies, entropy/area quantization, and greybody factor. We also analyze the behavior of the wave solutions near the event horizon of the rotating linear dilaton black hole and derive its Hawking t…
We investigate quasinormal modes, greybody factor, and Hawking evaporation of a five-dimensional Kerr-anti de Sitter (AdS$_5$) black hole by solving a wave equation for a test massive scalar field in terms of the local Heun function. We clarify the distribution of the quasinormal modes satisfying the ingoing and decaying boundary conditions at the event horizon and conformal infinity, respectively, and their splitting behaviors in the complex frequency plane with respect to a variation of spin parameters. We also point out the existence of purely imaginary modes. Further, we develop a method t…
Greybody factors in black hole physics modify the naive Planckian spectrum that is predicted for Hawking radiation when working in the limit of geometrical optics. We consider the Schwarzschild geometry in (3+1) dimensions, and analyze the Regge-Wheeler equation for arbitrary particle spin S and wave-mode angular momentum L, deriving rigourous bounds on the greybody factors as a function of S, L, wave frequency (omega), and the black hole mass, m.
In this work we derive a general expression for the greybody factor of non-minimally coupled scalar fields in Reissner-Nordström-de Sitter spacetime in low frequency approximation. In particular case of zero momentum, greybody factor tends to zero in low frequency limit as frequency squared goes to zero for non-vanishing coupling. We also elaborate the significance of the results by giving formulae of differential energy rate and general absorption cross section. The greybody factor gives insight into the spectrum of Hawking radiations.
We study the absorption probability and Hawking radiation of the scalar field in the rotating black holes on codimension-2 branes. We find that finite brane tension modifies the standard results in Hawking radiation if compared with the case when brane tension is completely negligible. We observe that the rotation of the black hole brings richer physics. Nonzero angular momentum triggers the super-radiance which becomes stronger when the angular momentum increases. We also find that rotations along different angles influence the result in absorption probability and Hawking radiation. Compared …
We investigate the effect of quantum correction on Hawking radiation for Schwarzschild black holes. We consider Hawking temperature and entropy to order G^2 and find that the area law of black holes should be modified. We think of Hawking radiation as tunneling and find that at certain frequency ω the radiation spectrum of black holes can be pure blackbody spectrum. Therefore, it is possible to break down information conservation. In order to ensure information conservation at any energy scales, we suggest that black holes cannot release all information they have. We briefly discuss the bound …
In this paper, we study the weak deflection angle of black hole in effective loop quantum gravity using the geometrical technique used by Gibbons and Werner. We first derive the optical metric, calculate the Gaussian optical curvature, and then apply the Gauss-Bonnet theorem. We then also investigate the effect of plasma and dark matter mediums on the weak deflection angle. We show that increasing the impact of these two mediums grows the deflection angle. We also calculate the Hawking temperature via Gauss-Bonnet theorem. In addition, we determine the fermionic greybody bounds. Moreover, we d…
We study the greybody factors of the scalar fields in spherically symmetric Einstein-Gauss-Bonnet-de Sitter black holes in higher dimensions. We derive the greybody factors analytically for both minimally and non-minimally coupled scalar fields. Moreover, we discuss the dependence of the greybody factor on various parameters including the angular momentum number, the non-minimally coupling constant, the spacetime dimension, the cosmological constant and the Gauss-Bonnet coefficient in detail. We find that the non-minimal coupling may suppress the Hawking radiation, while the Gauss-Bonnet coupl…
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.
Semiclassical black holes emit radiation called Hawking radiation. Such radiation, as seen by an asymptotic observer far outside the black hole, differs from original radiation near the horizon of the black hole by a redshift factor and the so-called "greybody factor". In this paper, we concentrate on the greybody factor-various bounds for the greybody factors of non-rotating black holes are obtained, concentrating on charged Reissner-Nordstrom and Reissner-Nordstrom-de Sitter black holes. These bounds can be derived by using a 2x2 transfer matrix formalism. It is found that the charges of bla…
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 derive the Hawking radiation power equations for black holes in asymptotically flat, asymptotically Anti-de Sitter (AdS) and asymptotically de Sitter (dS) black holes, This is done by using the greybody factor for these black holes. We observe that the radiation power equation for asymptotically flat black holes, corresponding to greybody factor at low frequency, depends on both the Hawking temperature and the horizon radius. However, for the greybody factors at asymptotic frequency, it only depends on the Hawking temperature. We also obtain the power equation for asymptotically AdS black h…
Extending a computation which appeared recently in hep-th/0301173, we compute the transmission and reflection coefficients for massless uncharged scalars and gravitational waves scattered by d>=4 Schwarzschild or d=4 Reissner-Nordstrom black holes, in the limit of large imaginary frequencies. The transmission coefficient has an interpretation as the "greybody factor" which determines the spectrum of Hawking radiation. The result has an interesting structure and we speculate that it may admit a simple dual description; curiously, for Reissner-Nordstrom the result suggests that this dual descrip…
We analytically study the low-frequency properties of the analogue Hawking effect in Bose-Einstein condensates. We show that in one-dimensional flows displaying an analogue horizon, the Hawking effect is dominant in the low-frequency regime. This happens despite non vanishing greybody factors, that is, the coupling of the Hawking mode and its partner to the mode propagating with the flow. To show this, we obtained analytical expressions for the scattering coefficients, in general flows and taking into account the full Bogoliubov dispersion relation. We discuss the obtained expressions for the …
In this study, we probe the weak lensing by a Reissner--Nordström black hole corrected by bounce parameter in plasma and dark matter mediums. For this, the optical geometry and the Gibbons--Werner approach are utilized to obtain the bending angle in the weak field limitations. We examine that the impact of these mediums increases the black hole's bending angle. In addition, we graphically study the deflection angle of light with respect to the impact parameter and examine that the bounce parameter directly affects the angle. Further, we compute the Hawking radiation via a topological method in…
We consider a massless, minimally coupled scalar field propagating through the geometry of a black 3-brane in an asymptotically $AdS_5 \times S^5$ space. The wave equation for modes traveling purely in the holographic direction reduces to a Heun equation and the corresponding greybody factor is obtained numerically. Approximations valid in the low- and high-frequency regimes are also obtained analytically. The greybody factor is then used to determine the rate of evaporation of these large black holes in the context of the evaporon model proposed in \cite{Rocha:2008fe}. This setting represents…
We study false vacuum decay catalyzed by black holes. We consider a toy two-dimensional model of a scalar field with an unstable potential in the background of a dilaton black hole. A realistic black hole in four dimensions possesses the potential barrier for linear field perturbations. We model this barrier -- the greybody factor -- for spherically-symmetric perturbations in the toy model by adding a coupling between the scalar field and dilaton. We compute analytically the decay rate for the black hole in thermal equilibrium (Hartle-Hawking state) and for the radiating black hole in empty sp…
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.
We study the sparsity of Hawking radiation from nonrotating singularity-free black holes in conformal gravity. We give a rigorous bound on the greybody factor for massless scalar field and calculate the sparsity of Hawking radiation from the black hole. Besides, we investigate the dependence of the greybody factor and the sparsity of Hawking radiation on the conformal parameters. Our study shows that the Hawking radiation from the black hole is extremely sparse. When the conformal parameters are large, the increase of conformal parameters will lead to an even more sparse Hawking radiation, whi…
The greybody factor from the black string in the de Rham-Gabadadze-Tolley (dRGT) massive gravity theory is investigated in this study. The dRGT massive gravity theory is one of the modified gravity theories used in explaining the current acceleration in the expansion of the universe. By using cylindrical symmetry, black strings in dRGT massive gravity are shown to exist. When quantum effects are taken into account, black strings can emit thermal radiation called Hawking radiation. The Hawking radiation at spatial infinity differs from that at the source by the so-called greybody factor. In thi…
We present the wave equation for a minimally coupled scalar field in the background of a rotating four-dimensional black hole that is parametrized by its mass, angular momentum, and four independent U(1) charges. The near horizon structure is identical to the five-dimensional case, and suggestive of an underlying description in string theory that is valid in the general non-extremal case. We calculate the greybody factors for the Hawking radiation. For sufficiently large partial wave number the emission spectrum can be calculated for general non-extremal black holes and any particle energy. We…
We study scalar perturbations of the five-dimensional rotating black holes and find an exact solution giving exact description of the Hawking radiation. Mathematically, the full solution for this s-wave mode is expressed in terms of the prolate spheroidal wave function with complex parameters. By using the spheroidal joining factor, we write the corresponding boundary condition and greybody factors. We also check that the exact result reproduces the low frequency limit of the greybody factor and shows good agreement with the known numerical results.
In recent work concerning the sparsity of the Hawking flux [arXiv:1506.03975v2], we found it necessary to re-examine what is known regarding the greybody factors of black holes, with a view to extending and expanding on some old results from the 1970s. Focussing specifically on Schwarzschild black holes, we re-calculated and re-assessed the greybody factors using a path-ordered-exponential approach, a technique which has the virtue of providing a semi-explicit formula for the relevant Bogoliubov coefficients. These path-ordered-exponentials, (being based on a "transfer matrix" formalism), are …
We compute the greybody factors for non-minimally coupled scalar fields in four-dimensional Schwarzschild-de Sitter spacetime. In particular, we demonstrate that the zero-angular-momentum greybody factor generically tends to zero in the zero-frequency limit like frequency squared if there is non-vanishing coupling to the scalar curvature. This is in contrast with the minimally coupled case, where the greybody factor is known to tend to a finite constant. We also study the Hawking radiation for non-minimally coupled massless scalar fields in Schwarzschild-de Sitter spacetime, formulate a sensib…
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…
Accretion, greybody factor, quasinormal modes, power spectrum, sparsity of Hawking radiation, and weak gravitational lensing of a minimum measurable length inspired Schwarzchild black hole
The production of black holes in extra-dimensional brane-world theories can lead to detectable signals via the Hawking evaporation of the black hole to brane-localised Standard Model modes. We calculate, as a function of partial wave number and number of toroidally compactified extra dimensions, the leading correction to the energy spectrum of such Hawking radiation (the greybody factors) for decay into spin 1/2 fermions and spin 1 gauge fields localised on the Standard Model brane. We derive the associated improved differential emission rates for both types of fields. We provide both simple e…
In this work we study the inverse problem related to the emission of Hawking radiation. We first show how the knowledge of greybody factors of different angular contributions $l$ can be used to constrain the width of the corresponding black hole perturbation potentials. Afterwards we provide a framework to recover the greybody factors from the actual energy emission spectrum, which has to be treated as sum over all multipole numbers. The underlying method for the reconstruction of the potential widths is based on the inversion of the Gamow formula, a parabolic expansion and the Pöschl-Teller p…
We construct a new exact solution in the 5D Einstein-Maxwell-dilaton gravity describing a magnetized squashed black hole. We calculate its physical characteristics, and derive the Smarr-like relations. The Hawking radiation of the solution is also investigated by calculating the greybody factor for the emission of massless scalar particles in the low-energy regime. In distinction to the case of asymptotically flat magnetized black holes, the thermodynamical characteristics and the Hawking radiation of the solution depend on the external magnetic field, and consequently can be tuned by its vari…
We investigate the Hawking radiation cascade from the five-dimensional charged black hole with a scalar field coupled to higher-order Euler densities in a conformally invariant manner. We give the semi-analytic calculation of greybody factors for the Hawking radiation. Our analysis shows that the Hawking radiation cascade from this five-dimensional black hole is extremely sparse. The charge enhances the sparsity of the Hawking radiation, while the conformally coupled scalar field reduces this sparsity.
The Myers-Perry black holes are higher-dimensional generalizations of the usual (3+1)-dimensional rotating Kerr black hole. They are of considerable interest in Kaluza-Klein models, specifically within the context of brane-world versions thereof. In the present article we shall consider the greybody factors associated with scalar field excitations of the Myers-Perry spacetimes, and develop some rigorous bounds on these greybody factors. These bounds are of relevance for characterizing both the higher-dimensional Hawking radiation, and the super-radiance, that is expected for these spacetimes.
We derive the wave equation for a minimally coupled scalar field in the background of a general rotating five-dimensional black hole. It is written in a form that involves two types of thermodynamic variables, defined at the inner and outer event horizon, respectively. We model the microscopic structure as an effective string theory, with the thermodynamic properties of the left and right moving excitations related to those of the horizons. Previously known solutions to the wave equation are generalized to the rotating case, and their regime of validity is sharpened. We calculate the greybody …
In the present article, we study the Hawking radiation (HR) of spin-1 particles -- so-called vector particles -- from a three dimensional (3D) rotating black hole with scalar hair (RBHWSH) using Hamilton-Jacobi (HJ) ansatz. Putting the Proca equation amalgamated with the WKB approximation in process, the tunneling spectrum of vector particles is obtained. We recover the standard Hawking temperature corresponding to the emission of these particles from RBHWSH.
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.
