The Stefan-Boltzmann law can estimate particle emission power and lifetime of a black hole. However, in modified gravity theories, new parameters in the action can cause qualitative changes in thermodynamic quantities, thus obtaining specific thermodynamic properties often requires complicated calculation with higher degree equations. In this work, we aim to provide a general model-independent description of the evolution of AdS black holes, using Gauss-Bonnet massive gravity as an example. We prove that the impact factor of an infinitely large AdS black hole is equal to the effective AdS radius, and the black hole is able to evaporate an infinite amount of mass in finite time, so that the lifetime of the black hole depends on the final state temperature in the evaporation process. The black hole will evaporate out when the final state temperature diverges and will transform into a remnant when the temperature is zero. Since we have analyzed massive gravity in detail, we can introduce the Gauss-Bonnet term to study how it affects the thermodynamic quantities. We obtain the final states for different parameter intervals, study the qualitative properties of black hole evaporation, and classify the associated cases. This method can also be applied to other models.
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…
We study the Hawking radiation in a new class of black hole solutions in the Einstein-Gauss-Bonnet theory. The black hole has been argued to have vanishing mass and entropy, but finite Hawking temperature. To check if it really emits radiation, we analyse the Hawking radiation using the original method of quantization of scalar field in the black hole background and the quantum tunneling method, and confirm that it emits radiation at the Hawking temperature. A general formula is derived for the Hawking temperature and backreaction in the tunneling approach. Physical implications of these resul…
We show that although generalized uncertainty principle with negative parameter allows black holes to evaporate completely, this process takes an infinite amount time to achieve, resulting in a metastable remnant.
The $(3+1)$-dimensional Einstein-Gauss-Bonnet theory of gravity which breaks the Lorentz invariance in a theoretically consistent and observationally viable way has been recently suggested by Aoki, Gorji and Mukohyama [arXiv:2005.03859]. Here we calculate grey-body factor for Dirac, electromagnetic and gravitational fields and estimate the intensity of Hawking radiation and lifetime for asymptotically flat black holes in this theory. Positive coupling constant leads to much smaller evaporation rate and longer life-time of a black hole, while the negative one enhances Hawking radiation. The gre…
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…
Inspired by string theory, Heisenberg's uncertainty principle can be generalized to include the photon-electron gravitational interaction, which leads to the Generalized Uncertainty Principle (GUP). Although GUP considers gravitational uncertainty at the minimum fundamental length scale in physics, it does not consider the effects of spacetime curvature on quantum mechanical uncertainty relations. The Extended Uncertainty Principle (EUP) is a generalization of Heisenberg's Uncertainty Principle that, unlike the GUP, applies to large length scales. GEUP is also a linear combination of EUP and G…
For an extreme charged black hole some scalars take on a fixed value at the horizon determined by the charges alone. We call them fixed scalars. We find the absorption cross section for a low frequency wave of a fixed scalar to be proportional to the square of the frequency. This implies a strong suppression of the Hawking radiation near extremality. We compute the coefficient of proportionality for a specific model.
It is well-known that there exists a Hawking-Page phase transition between a spherical AdS black hole and a thermal AdS space. The phase transition does not happen between a Ricci flat AdS black hole whose horizon is a Ricci flat space and a thermal AdS space in the Poincare coordinates. However, the Hawking-Page phase transition occurs between a Ricci flat AdS black hole and an AdS soliton if at least one of horizon coordinates for the Ricci flat black hole is compact. We show a similar phase transition betwen the Ricci flat black holes and deformed AdS solitons in the Gauss-Bonnet gravity an…
Einstein-Gauss-Bonnet theory is a string-generated gravity theory when approaching the low energy limit. By introducing the higher order curvature terms, this theory is supposed to help to solve the black hole singularity problem. In this work, we investigate the evaporation of the static spherically symmetric neutral AdS black holes in Einstein-Gauss-Bonnet gravity in various spacetime dimensions with both positive and negative couping constant $α$. By summarizing the asymptotic behavior of the evaporation process, we find the lifetime of the black holes is dimensional dependent. For $α>0$, i…
We investigate the probabilities of the tunneling and the radiation spectrums of the massive spin-1 particles from arbitrary dimensional Gauss-Bonnet-Axions (GBA) Anti-de Sitter (AdS) black brane, via using the WKB approximation to the Proca spin-1 field equation. The tunneling probabilities and Hawking temperature of the arbitrary dimensional GBA AdS black brane is calculated via the Hamilton-Jacobi approach. We also compute the Hawking temperature via Parikh-Wilczek tunneling approach. The results obtained from the two methods are consistent. In our setup, the Gauss-Bonnet (GB) coupling affe…
We study the Hawking evaporation of a class of black hole solutions in dRGT massive gravity, in which the graviton mass gives rise to an effective negative cosmological constant. We found that the effective emission surface can be either proportional to the square of the effective AdS length scale, or corresponds to the square of the impact parameter of the null geodesic that falls onto the photon orbit of the black hole. Furthermore, depending on the black hole parameters, the emission surface could switch from one to another as the black hole loses mass during the evaporation process. Furthe…
It is shown that rapidly-rotating Kerr black holes are characterized by the dimensionless ratio $τ_{\text{gap}}/τ_{\text{emission}}=O(1)$, where $τ_{\text{gap}}$ is the average time gap between the emission of successive Hawking quanta and $τ_{\text{emission}}$ is the characteristic timescale required for an individual Hawking quantum to be emitted from the black hole. This relation implies that the Hawking cascade from rapidly-rotating black holes has an almost continuous character. Our results correct some inaccurate claims that recently appeared in the literature regarding the nature of the…
We obtain an exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled with nonlinear electrodynamics with the Lagrangian ${\cal L}_{NED} = -{\cal F}/(1+\sqrt{2\midβ{\cal F}\mid})$ (${\cal F}$ is the field strength invariant). The thermodynamics of the black hole is studied within our model. We calculate the Hawking temperature and the heat capacity of the black hole. The phase transitions occur in the point where the Hawking temperature possesses an extremum and the heat capacity diverges. It was shown that black holes are thermodynam…
The semi-classical Hawking evaporation process of Reissner-Nordström black holes is analyzed. It is shown that this quantum mechanism may turn a near-extremal black-hole spacetime with $T_{\text{BH}}\lesssim \hbar^2/G^2M^3$ into an horizonless naked singularity, thus violating the Penrose cosmic censorship conjecture. It is therefore conjectured that, within the framework of a self-consistent quantum theory of gravity, the Bekenstein-Hawking temperature should be bounded from below by the simple relation $T_{\text{BH}}\gtrsim \hbar^2/G^2M^3$.
We discuss semiclassical Nariai black holes in the framework of $f(T)$-gravity. For a diagonal choice of tetrades, stable Nariai metrics can be found, emitting Bekenstein-Hawking radiation in semiclassical limit. However, for a non-diagonal choice of tetrades, evaporation and antievaporation instabilities are turned on. In turn, this causes a back-reaction effect suppressing the Bekenstein-Hawking radiation. In particular, evaporation instabilities produce a new radiation -- different by Bekenstein-Hawking emission -- non-violating unitarity in particle physics sector.
We study the cascade of Hawking emission spectrum from the event horizon in presence of one loop back reaction effect in a black hole background. The spacetime is taken here is the modified Schwarzschild one. The analysis shows that it is possible to decrease the sparsity with the decrease in black hole mass. Moreover, at some particular value of mass one has a continuous radiation cascade. This result is completely new and quite different from the usual one. An estimation of the mass for continuous one is also found. We see that the value is of the Planck mass order. In this process it is obs…
Classical (quasinormal) and quantum (Hawking) radiations are investigated for test fields in the background of a four dimensional, spherically symmetric and asymptotically flat black hole in the Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The geometry of the EdGB black hole deviates from the Schwarzschild geometry only slightly. Therefore, here we observe that the quasinormal spectrum also deviates from its Schwarzschild limit at most moderately, allowing for a $9\%$ decrease in the damping rate and up to a $6\%$ decrease in the real oscillation frequency. However, the intensity of Hawking ra…
Contradiction between Hawking's semi-classical arguments and string theory on the evaporation of black hole has been one of the most intriguing problems in fundamental physics. A final-state boundary condition inside the black hole was proposed by Horowitz and Maldacena to resolve this contradiction. We point out that original Hawking effect can be also regarded as a separate boundary condition at the event horizon for this scenario. Here, we found that the change of Hawking boundary condition may affect the information transfer from the initial collapsing matter to the outgoing Hawking radiat…
In this paper, the Hawking-Page phase transitions between the black holes and thermal anti-de Sitter (AdS) space are studied with the Gauss-Bonnet term in the extended phase space, in which the varying cosmological constant plays the role of an effective thermodynamic pressure. The Gauss-Bonnet term exhibits its effects via introducing the corrections to the black hole entropy and Gibbs free energy. The global phase structures, especially the phase transition temperature $T_{\rm HP}$ and the Gibbs free energy $G$, are systematically investigated, first for the Schwarzschild-AdS black holes and…
The thermodynamics and the kinetics of Hawking-Page phase transition were studied previously based on the free energy landscape. The AdS black hole can evaporate if imposing the absorbing boundary conditions at infinity. We suggest that the kinetics of Hawking-Page phase transition should be governed by the reaction-diffusion equation, where the Hawking evaporation plays the role of the reaction on the background of the free energy landscape. By calculating the mean first passage time from the large black hole phase to the thermal gas phase, we show that the phase transition can occur more eas…
Exponentially Long Evaporation of Noncommutative Black Hole
National Taiwan University（国立台湾大学）；National Center for Theoretical Sciences（国家理论科学中心）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论与数学科学中心(iTHEMS)）；Kyoto University（京都大学）
The Hawking-Page (HP) phase transitions of the anti-de Sitter black holes in the extended phase space are studied in a novel four-dimensional Einstein-Gauss-Bonnet (4EGB) gravity, which is proposed by rescaling the Gauss--Bonnet (GB) coupling constant $α\toα/(d-4)$ in $d$ dimensions and redefining the four-dimensional gravity in the limit $d \to 4$. The GB term shows nontrivial contributions to both black hole mass and entropy simultaneously, and decreases the HP phase transition temperature $T_{\rm HP}$. Moreover, the HP phase transitions can happen only within a range of pressure in the 4EGB…
It was recently pointed out that if an absorbing boundary condition is imposed at infinity, an asymptotically anti-de Sitter Schwarzschild black hole with a spherical horizon takes only a finite amount of time to evaporate away even if its initial mass is arbitrarily large. We show that this is a rather generic property in AdS spacetimes: regardless of their horizon topologies, neutral AdS black holes in general relativity take about the same amount of time to evaporate down to the same size of order L, the AdS length scale. Our discussion focuses on the case in which the black hole has toral …
We study evaporation process of black strings which are typical examples of Kaluza-Klein black holes. Taking into account the backreaction of the Hawking radiation, we deduce the evolution equation for the radion field. By solving the evolution equation, we find that the shape of the internal space is necked by the Hawking radiation and the amount of the deformation becomes large as the evaporation proceeds. Based on this analysis, we speculate that the Kaluza-Klein black holes would be excised from the Kaluza-Klein spacetime before the onset of the Gregory-Laflamme instability and therefore b…
Hawking's seminal discovery of black hole evaporation was based on the semi-classical, perturbative method. Whether black hole evaporation may result in the loss of information remains undetermined. The solution to this paradox would most likely rely on the knowledge of the end-life of the evaporation, which evidently must be in the non-perturbative regime. Here we reinterpret the Hawking radiation as the tunneling of instantons, which is inherently non-perturbative. For definitiveness, we invoke the picture of shell-anti-shell pair production and show that it is equivalent to that of instanto…
There have been various interpretations of Hawking radiation proposed based on the perturbative approach, and all have confirmed Hawking's original finding. One major conceptual challenge of Hawking evaporation is the associated black hole information loss paradox, which remains unresolved. A key factor to the issue is the end-stage of the black hole evaporation. Unfortunately by then the evaporation process becomes non-perturbative. Aspired to provide a tool for the eventual solution to this problem, here we introduce a new interpretation of Hawking radiation as the tunneling of instantons. W…
We discuss black holes in an effective theory derived from a superstring model, which includes a dilaton field, a gauge field and the Gauss-Bonnet term. Assuming U(1) or SU(2) symmetry for the gauge field, we find four types of spherically symmetric solutions, i.e., a neutral, an electrically charged, a magnetically charged and a ``colored'' black hole, and discuss their thermodynamical properties and fate via the Hawking evaporation process. For neutral and electrically charged black holes, we find critical point and a singular end point. Below the mass corresponding to the critical point, no…
By using a new approach, we demonstrate analytic expressions for slowly rotating Gauss-Bonnet charged black holes with negative cosmological constant. Up to the linear order of the rotating parameter a, the mass, Hawking temperature and entropy of the charged black holes get no corrections from rotation.
In this paper, a new family of Hawking-Page (HP) transition, the HP transition with reentrance and triple point is introduced for the first time, by investigating HP transition of hyperbolic AdS black hole in extended thermodynamics of general dimensional Gauss-Bonnet gravity. The Reentrant HP transition is composed of two HP transitions with a large and a small HP temperature, and the triple point corresponds to small black holes/massless black holes/large black holes (SBHs/MBHs/LBHs) phases all coexisting. We present the two branches of HP transition temperatures, which both depend on the pr…
The quantum stress-energy tensor of a massless scalar field propagating in the two-dimensional Vaidya-de Sitter metric, which describes a classical model spacetime for a dynamical evaporating black hole in an inflationary universe, is analyzed. We present a possible way to obtain the Hawking radiation terms for the model with arbitrary functions of mass. It is used to see how the expansion of universe will affect the dynamical process of black hole evaporation. The results show that the cosmological inflation has an inclination to depress the black hole evaporation. However, if the cosmologica…
When a black hole is in an empty space on which there is no matter field except that of the Hawking radiation (Hawking field), then the black hole evaporates and the entropy of the black hole decreases. The generalised second law guarantees the increase of the total entropy of the whole system which consists of the black hole and the Hawking field. That is, the increase of the entropy of the Hawking field is faster than the decrease of the black hole entropy. In naive sense, one may expect that the entropy increase of the Hawking field is due to the self-interaction among the composite particl…
Exciting peculiarities of Planck-scale physics have immediate effects on the Bekenstein-Hawking radiation emitted from black holes (BHs). In this paper, using the tunneling formalism, we determine the Bekenstein-Hawking temperature for the vector particles from a backreacted black hole (BBH) constructed from a conformal scalar field surrounded by a BTZ (Banados-Teitelboim-Zanelli) BH. Then, under the effect of the generalized uncertainty principle, we extend our calculations for scalar particles to understand the effects of quantum gravity. Then, we calculate an evaporation time for the BBH, t…
We explore the Hawking evaporation of two-dimensional anti-de Sitter (AdS$_2$), dilatonic black hole coupled with conformal matter, and derive the Page curve for the entanglement entropy of radiation. We first work in a semiclassical approximation with backreaction. We show that the end-point of the evaporation process is AdS$_2$ with a vanishing dilaton, i.e. a regular, singularity-free, zero-entropy state. We explicitly compute the entanglement entropies of the black hole and the radiation, as functions of the horizon radius, using the conformal field theory (CFT) dual to AdS$_2$ gravity. We…
One of the most intriguing problem of modern physics is the question of the endpoint of black hole evaporation. Based on Einstein-dilaton-Gauss-Bonnet four dimensional string gravity model we show that black holes do not disappear and that the end of the evaporation process leaves some relic. The possibility of experimental detection of the remnant black holes is investigated. If they really exist, such objects could be a considerable part of the non baryonic dark matter in our Universe.
We analyze the Hawking evaporation process of Reissner-Nordström black holes. It is shown that the characteristic radiation quanta emitted by the charged black holes may turn near-extremal black-hole spacetimes into horizonless naked singularities. The present analysis therefore reveals the intriguing possibility that the semi-classical Hawking evaporation process of black holes may violate the fundamental Penrose cosmic censorship conjecture.
A simple classical consideration of black hole formation and evaporation times focusing solely on the frame of an observer at infinity demonstrates that an infall cutoff outside the event horizon of a black hole must be imposed in order for the formation time of a black hole event horizon to not exceed its evaporation time. We explore this paradox quantitatively and examine possible cutoff scales and their relation to the Planck scale. Our analysis suggests several different possibilities, none of which can be resolved classically and all of which require new physics associated with even large…
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…
A reformulation of the calculation of the semi-classical energy-momentum tensor on a Schwarzschild background, the Bousso covariant entropy bound, and the ER=EPR conjecture of Maldacena and Susskind taken together suggest a scenario for the evaporation of a large spherically symmetric black hole formed in gravitational collapse in which 1) the classical r = 0 singularity is replaced by an initially small non-singular core inside an inner apparent horizon, 2) the radius of the core grows with time due to the increasing entanglement between Hawking radiation quanta outside the black hole and the…
We study Hawking radiation on a Vaidya space-time with a gravitational collapse followed by evaporation. The collapsing body is a null thin-shell and the evaporation is induced by a negative energy collapsing null-shell. This mimics the back-reaction to the Hawking radiation. Using Hawking's original method of Bogoliubov transformations we characterize the radiated spectrum as dominated by a thermal emission with an increasing effective temperature. We compute this time dependent temperature and find numerical agreement with results obtained by other techniques. The known divergences at the ev…
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…
We explicitly describe the last stages of black hole evaporation in the context of string theory : the combined study of Quantum Field Theory (QFT) and String Theory (ST) in curved backgrounds allows us to go further in the understanding of quantum gravity effects. The string ``analogue model''(or thermo-dynamical approach) is a well suited framework for this purpose.The results also apply to another physically relevant case: de Sitter background. Semiclassical (QFT) and quantum gravity (String) phases or regimes are properly determined (back reaction effects included). The Hawking-Gibbons tem…
When a black hole is put in an "empty" space (zero temperature space) on which there is no matter except the matter of the Hawking radiation (Hawking field), then an outgoing energy flow from the black hole into the empty space exists. By the way, an equilibrium between two arbitrary systems can not allow the existence of an energy (heat) flow from one system to another. Consequently, in the case of a black hole evaporation in the empty space, the Hawking field should be in a nonequilibrium state. Hence the total behaviour of the evaporation, for example the time evolution of the total entropy…
