We extend the classic results of the paper P. C. W. Davies, S. A. Fulling, and W. G. Unruh "Energy-momentum tensor near an evaporating black hole" by considering a massive scalar field in a two dimensions in the presence of a thin shell collapse. We show that outside the shell the WKB approximation is valid for any value of $r$ if $mr_{g} \gg 1$, where $m$ is the mass of the field, and $r_{g}$ is the Schwarzschild radius. Thus, we use semiclassical modes to calculate the flux in the vicinity of the shell, and at spatial infinity, $r \rightarrow +\infty$ at the final stage of the collapse, $t \rightarrow +\infty$ with the use of the covariant point-splitting regularization. We get that near the shell and at the spatial infinity the radiation is thermal with Hawking temperature. We obtain the negative flux $T_{vv}$ in the vicinity of the shell, which is similar to the classic result in the massless case.
Locality plays a key role in the derivation of Hawking radiation. Could relaxing the locality criterion modify Hawking radiation? We consider Hawking radiation in a general class of non local quantum field theories. We prove that Hawking radiation is unmodified for these theories. Our result establishes the universality of Hawking radiation in a larger class of theories.
Generalising the method of Wilczek and collaborators we provide a derivation of Hawking radiation from charged black holes using only covariant gauge and gravitational anomalies. The reliability and universality of the anomaly cancellation approach to Hawking radiation is also discussed.
Hawking radiation is one of the cores in modern gratitational theory. Several articles have calculated the spectrum of Hawking radiation in Boltzmann-Gibbs statistical mechanics. However, based on recent researches, gravitational systems cannot be studied by the standard statistical mechanics. In this article, we calculate the modification to the spectrum of Hawking radiation in Tsallis statistical mechanics. We obtain the modified Stefan-Boltzmann's law and modified power of Hawking radiation. We confirm the conclusion proposed by Giddings, namely, the radiation should originate from the effe…
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.
In completely local settings, we establish that a dynamically evolving black hole horizon can be assigned a Hawking temperature. Moreover, we calculate the Hawking flux and show that the radius of the horizon shrinks.
We study the time-dependence of Hawking radiation for a black hole in the Unruh vacuum, and find that it is not robust against certain UV and IR effects. If there is a UV cutoff at the Planck scale, Hawking radiation is turned off after the scrambling time. In the absence of a UV cutoff, Hawking radiation is sensitive to the IR cutoff through a UV/IR connection due to higher-derivative interactions in the effective theory. Furthermore, higher-derivative interactions with the background contribute to a large amplitude of particle creation that changes Hawking radiation. This unexpected large ef…
From appropriate expressions for effective actions, the Hawking radiation from charged black holes is derived, using only covariant boundary conditions at the event horizon. The connection of our approach with the Unruh vacuum and the recent analysis \cite{Robwilczek,Isowilczek,shailesh} of Hawking radiation using anomalies is established.
We study the greybody factor and Hawking radiation with a non-minimal derivative coupling between the scalar field and the curvature in the background of the slowly rotating Kerr-Newman black hole. Our results show that both the absorption probability and luminosity of Hawking radiation of the scalar field increase with the coupling. Moreover, we also find that for the weak coupling $η<η_c$, the absorption probability and luminosity of Hawking radiation decrease when the black hole's Hawking temperature decreases; while for stronger coupling $η>η_c$, the absorption probability and luminosity o…
We study the Hawking thermal spectrum in dragging coordinate system and the tunneling radiation characteristics of hot NUT-Kerr-Newman-Kasuya spacetime. The tunneling rates at the event and cosmological horizon are found to be related to the change of Bekenstein-Hawking entropy. The radiation spectrum is not pure thermal and thus there is a correction to the Hawking thermal spectrum.
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.
We study the Hawking radiation from Rotating black holes from gravitational anomalies point of view. First, we show that the scalar field theory near the Kerr black hole horizon can be reduced to the 2-dimensional effective theory. Then, following Robinson and Wilczek, we derive the Hawking flux by requiring the cancellation of gravitational anomalies. We also apply this method to Hawking radiation from higher dimensional Myers-Perry black holes. In the Appendix, we present the trace anomaly derivation of Hawking radiation to argue the validity of the boundary condition at the horizon.
We provide a simple way for calculating the entropy of a Schwarzschild black hole from the entropy of its Hawking radiation. To this end, we show that if a thermodynamic system loses its energy only through the black body radiation, its loss of entropy is always 3/4 of the entropy of the emitted radiation. This proposition enables us to relate the entropy of an evaporating black hole to the entropy of its Hawking radiation. Explicitly, by calculating the entropy of the Hawking radiation emitted in the full period of evaporation of the black hole, we find the Bekenstein-Hawking entropy of the i…
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 explore the obsevability of extra dimensions through 5-dimensional squashed Kaluza-Klein black holes residing in the Kaluza-Klein spacetime. With the expectation that the Hawking radiation reflects the 5-dimensional nature of the squashed horizon, we study the Hawking radiation of a scalar field in the squashed black hole background. As a result, we show that the luminosity of Hawking radiation tells us the size of the extra dimension, namely, the squashed Kaluza-Klein black holes open a window to extra dimensions.
We show that for the thermal spectrum of Hawking radiation black hole's information loss paradox may still be present, even if including the entanglement information stored in the entangled Minkowski vacuum. And to avoid this inconsistency, the spectrum of Hawking radiation must be nonthermal. After reconsidering the derivation of Hawking effect, we find that the thermal spectrum is actually resulted from the geometric optics approximation in deriving the Bogolubov coefficients. When treated a little more accurately, we obtain some nonthermal spectrum for the Hawing radiation, which reduces to…
We study various derivations of Hawking radiation in conformally rescaled metrics. We focus on two important properties, the location of the horizon under a conformal transformation and its associated temperature. We find that the production of Hawking radiation cannot be associated in all cases to the trapping horizon because its location is not invariant under a conformal transformation. We also find evidence that the temperature of the Hawking radiation should transform simply under a conformal transformation, being invariant for asymptotic observers in the limit that the conformal transfor…
We give a detailed treatment of the back-reaction effects on the Hawking spectrum in the semiclassical approach to the Hawking radiation. We solve the exact system of non linear equations giving the action of the system, by a rigorously convergent iterative procedure. The first two terms of such an expansion give the O(omega/M) correction to the Hawking spectrum.
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 derive Hawking radiation of 5-dimensional black rings from gauge and gravitational anomalies using the method proposed by Robinson and Wilczek. We find as in the black hole case, the problem could reduce to a (1+1) dimensional field theory and the anomalies result in correct Hawking temperature for neutral,dipole and charged black rings.
Proceedings of the 'Hawking Radiation' conference in Stockholm, Sweden 2015. It includes a link to the video recording of the conference and all the talks, discussions, and communications, that took place during the week of the conference . We hope the recorded discussions will be helpful, especially to the current and future young researchers and students.
We present a model for cosmological inflation which has a natural "turn on" and a natural "turn off" mechanism. In our model inflation is driven by the Hawking-like radiation that occurs in Friedman-Robertson-Walker (FRW) space-time. This Hawking-like radiation results in an effective negative pressure "fluid" which leads to a rapid period of expansion in the very early Universe. As the Universe expands the FRW Hawking temperature decreases and the inflationary expansion turns off and makes a natural transition to the power law expansion of a radiation dominated universe. The "turn on" mechani…
In this review, we describe recent progress on the black hole information problem that involves a new understanding of how to calculate the entropy of Hawking radiation. We show how the method for computing gravitational fine-grained entropy, developed over the past 15 years, can be extended to capture the entropy of Hawking radiation. This technique reveals large corrections needed for the entropy to be consistent with unitary black hole evaporation.
We re-examine vacuum polarisation of a scalar field in a quasi-local volume including the horizon. We find that Hawking radiation rate is derived as a pure decay of vacuum due to scalar field interaction with classical gravity exactly in the same way as the origin of vacuum polarisation effect in Electrodynamics.
We study the method of calculating the Hawking radiation via gravitational anomalies in gravitational backgrounds of constant negative curvature. We apply the method to topological black holes and also to topological black holes conformally coupled to a scalar field.
In this paper we revisited Hawking radiation in the light of the original calculations of Hawking and Wald and found that some additional insights can be gained. We review a "derivation" of the field theory Hilbert space from the space of solutions, followed by the calculation of Bogoliubov coefficients in a collapsed spacetime from first principles. We show that these calculations can be generalized to the case of local Killing horizons and also to asymptotically non-flat spaces.
I present a new derivation of Hawking radiation by applying the Crooks fluctuation theorem to the laws of black hole thermodynamics. Then, by analogy with the quantum fluctuation theorem, this allows one to identify microstates contributing to the black hole entropy. These microstates have an evolution operator on the horizon between initial and final states that is related to the entropic gravity proposal. Their full calculation perhaps requires a deeper understanding of nonperturbative Hawking radiation.
Hawking radiation is computed in different coordinate systems using the method of complex paths. In this procedure the event horizon of the 2D Schwarzschild stringy black hole is treated as a singularity for the semiclassical action functional. After the regularization of the event horizon's singularity the emission/absorption probabilities and the Hawking temperature in the different coordinate representations are derived. The identical results obtained indicate the covariance of the Hawking radiation.
The purpose of this paper is to analyse the back reaction problem, between Hawking radiation and the black hole, in a simplified model for the black hole evaporation in the quantum geometrodynamics context. The idea is to transcribe the most important characteristics of the Wheeler-DeWitt equation into a Schrödinger's type of equation. Subsequently, we consider Hawking radiation and black hole quantum states evolution under the influence of a potential that includes back reaction. Finally, entropy is estimated as a measure of the entanglement between the black hole and Hawking radiation states…
We derive the Hawking radiation spectrum of anyons, namely particles in (2+1)-dimension obeying fractional statistics, from a Bañados, Teitelboim, and Zanelli (BTZ) black hole, in the tunneling formalism. We examine ways of measuring the spectrum in experimentally realizable systems in the laboratory.
We discuss an ambiguity of the derivation of the Hawking radiation through the gravitational anomaly method and propose modifications of this method such that it reproduces the correct thermal fluxes. In this modified gravitational anomaly method, we employ the two-dimensional conformal field theory technique.
In order to understand a boundary description of Hawking radiation in the AdS/CFT correspondence, we investigate the trace anomaly method in AdS$_2$ space. In this method, Hawking radiation is derived from the trace anomaly of the energy-momentum tensor in the bulk. We find a correspondence between the energy-momentum tensor and a composite operator in CFT$_1$ and understand the anomalous properties of the energy-momentum tensor in terms of this composite operator. By using this correspondence, we reproduce Hawking radiation from the boundary description. In addition, we find a correspondence …
Using the formalism that separates the contributions of vacuum fluctuations and radiation reaction to the rate of change of the mean atomic energy, we show that a two-level atom in interaction with a quantum massless scalar field both in the Hartle-Hawking and Unruh vacuum in a 1+1 dimensional black hole background spontaneously excites as if there is thermal radiation at the Hawking temperature emanating from the black hole. Our calculation, therefore, ties the existence of Hawking radiation to the spontaneous excitation of a two-level atom placed in vacuum in the exterior of a black hole and…
Recently proposed 2D anomaly induced effective actions for the matter-gravity system are critically reviewed. Their failure to correctly reproduce Hawking's black hole radiation or the stability of Minkowski space-time led us to a modification of the relevant ``quantum'' matter stress energy tensor that allows physically meaningful results to be extracted.
We calculate the quantum radiation from the five dimensional charged rotating black rings by demanding the radiation to eliminate the possible anomalies on the horizons. It is shown that the temperature, energy flux and angular-momentum flux exactly coincide with those of the Hawking radiation. The black rings considered in this paper contain the Myers-Perry black hole as a limit and the quantum radiation for this black hole, obtained in the literature, is recovered in the limit. The results support the picture that the Hawking radiation can be regarded as the anomaly eliminator on horizons an…
Hawking radiation emanating from two-dimensional charged and uncharged dilatonic black holes - dimensionally reduced from (2+1) spinning and spinless, respectively, BTZ black holes - is viewed as a tunnelling process. Two dimensional dilatonic black holes (AdS(2) included) are treated as dynamical backgrounds in contrast to the standard methodology where the background geometry is fixed when evaluating Hawking radiation. This modification to the geometry gives rise to a nonthermal part in the radiation spectrum. Nonzero temperature of the extremal two-dimensional charged black hole is found. T…
Hawking radiation from an evaporating black hole has often been compared to black body radiation. However, this comparison misses an important feature of Hawking radiation: Its low density of states. This can be captured in an easy to calculate, heuristic, and semi-analytic measure called "sparsity". In this letter we shall present both the concept of sparsities and its application to $D+1$-dimensional Tangherlini black holes and their evaporation. In particular, we shall also publish for the first time sparsity expressions taking into account in closed form effects of non-zero particle mass. …
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…
Where does Hawking radiation originate? A common picture is that it arises from excitations very near or at the horizon, and this viewpoint has supported the "firewall" argument and arguments for a key role for the UV-dependent entanglement entropy in describing the quantum mechanics of black holes. However, closer investigation of both the total emission rate and the stress tensor of Hawking radiation supports the statement that its source is a near-horizon quantum region, or "atmosphere," whose radial extent is set by the horizon radius scale. This is potentially important, since Hawking rad…
A recently discovered classical-quantum correspondence (CQC) maps certain quantum problems to corresponding classical problems. We illustrate the CQC for a quantum scalar field in the gravitational background of a collapsing spherical shell. By truncating the problem to a small set of variables, we show how the CQC can yield Hawking radiation as well as the slow down of the collapse due to radiation backreaction.
We give a higher-spin generalization of the anomaly method for the Hawking radiation from black holes. In the paper arXiv:0710.0453 higher-spin generalizations of the gauge (and gravitational) anomalies in d=2 were obtained. By applying these anomalies to black hole physics, we derive the higher moments of the Hawking fluxes. We also give a higher-spin generalization of the trace anomaly method by Christensen and Fulling.
By entangling soft massless particles one can create an arbitrarily large amount of entanglement entropy that carries an arbitrarily small amount of energy. Dropping this entropy into the black hole (b.h.) one can increase the b.h. entropy by an amount that violates Bekenstein bound or any other reasonable bound, leading to a version of b.h. information paradox that does not involve Hawking radiation. Among many proposed solutions of the standard b.h. information paradox with Hawking radiation, only a few can also resolve this version without the Hawking radiation. The assumption that both ver…
Recently, the relation between Hawking radiation and gravitational anomalies has been used to estimate the flux of Hawking radiation for a large class of black objects. In this paper, we extend the formalism, originally proposed by Robinson and Wilczek, to the Hawking radiation of vector particles (photons). It is explicitly shown, with Hamiltonian formalism, that the theory of an electromagnetic field on d-dimensional spherical black holes reduces to one of an infinite number of massive complex scalar fields on 2-dimensional spacetime, for which the usual anomaly-cancellation method is availa…
Hawking radiation of the blackhole is calculated based on the principle of local field theory. In our approach, the radiation is a unitary process, therefore no information loss will be recorded. In fact, observers in different regions of the space communicate using the Hawking radiation, when the systems in the different regions are entangled with each other. The entanglement entropy of the blackhole is also calculated in the local field theory. We found that the entanglement entropy of the systems separated by the blackhole horizon is closely connected to the Hawking radiation in our approac…
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…
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 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…
he quasi-classical method of deriving Hawking radiation is investigated. In order to recover the original Hawking temperature one must take into account a previously ignored contribution coming from the temporal part of the action. This contribution plus a contribution coming from the spatial part of the action gives the correct temperature.
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 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 …
There are numerous derivations of the Hawking effect available in the literature. They emphasise different features of the process, and sometimes make markedly different physical assumptions. This article presents a ``minimalist'' argument, and strips the derivation of as much excess baggage as possible. All that is really necessary is quantum physics plus a slowly evolving future apparent horizon (*not* an event horizon). In particular, neither the Einstein equations nor Bekenstein entropy are necessary (nor even useful) in deriving Hawking radiation.
We consider the island formula for the entropy of subsets of the Hawking radiation in the adiabatic limit where the evaporation is very slow. We find a simple concrete `on-shell' formula for the generalized entropy which involves the image of the island out in the stream of radiation, the `island in the stream'. The resulting recipe for the entropy allows us to calculate the quantum information properties of the radiation and verify various constraints including the Araki-Lieb inequality and strong subadditivity.
Incorporating Parikh and Wilczek's opinion to the Kerr de-Sitter (KdS) black hole Hawking non-thermal and purely thermal radiations have been investigated using Hamilton-Jacobi method. We have taken the background spacetime of KdS black hole as dynamical, involving the self-gravitation effect of the emitted particles, energy and angular momentum has been taken as conserved and show that the tunneling rate is related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum. The explored results gives a correction to the Hawking radiat…
Hawking radiation is studied for arbitrary scalars, fermions, and spin-1 bosons, using a tunneling approach, to every order in $\hbar$ but ignoring back-reaction effects. It is shown that the additional quantum terms yield no new contribution to the Hawking temperature. Indeed, it is found that the limit of small $\hbar$ in the standard quantum WKB approximation is replaced by the near-horizon limit in the gravitational WKB approach.
Hawking radiation is an important quantum phenomenon of black hole, which is closely related to the existence of event horizon of black hole. The cosmological event horizon of de Sitter space is also of the Hawking radiation with thermal spectrum. By use of the tunneling approach, we show that there is indeed a Hawking radiation with temperature, $T=1/2π\tilde r_A$, for locally defined apparent horizon of a Friedmann-Robertson-Walker universe with any spatial curvature, where $\tilde r_A$ is the apparent horizon radius. Thus we fill in the gap existing in the literature investigating the relat…
We investigate the Generalized Uncertainty Principle (GUP) effect on the Hawking radiation of the 2+1 dimensional Martinez-Zanelli black hole by using the Hamilton-Jacobi method. In this connection, we discuss the tunnelling probabilities and Hawking temperature of the spin-1/2 and spin-0 particles for the black hole. Therefore, we use the modified Klein-Gordon and Dirac equations based on the GUP. Then, we observe that the Hawking temperature of the scalar and Dirac particles depend on not only the black hole properties, but also the properties of the tunnelling particle, such as angular mome…
In the present paper we investigate the Hawking radiation of asymptotically non-flat dyonic black holes in 4D Einstein-Maxwell-dilaton gravity in semi-classical approximation. We show that the problem allows an exact analytical treatment and we compute exactly the semi-classical radiation spectrum of both non-extremal and extremal black holes under consideration. In the high frequency regime we find that the Hawking temperature does not agree with the surface gravity when the magnetic charge is nonzero. Even more surprisingly the Hawking temperature is independent of the black hole intrinsic c…
We discuss Hawking radiation from a five-dimensional squashed Kaluza-Klein black hole on the basis of the tunneling mechanism. A simple manner, which was recently suggested by Umetsu, is possible to extend the original derivation by Parikh and Wilczek to various black holes. That is, we use the two-dimensional effective metric, which is obtained by the dimensional reduction near the horizon, as the background metric. By using same manner, we derive both the desired result of the Hawking temperature and the effect of the back reaction associated with the radiation in the squashed Kaluza-Klein b…
