We derive the general form of Hawking temperature for Vaidya black hole in the tunneling pictures. This kind of black hole is regarded as the description of a more realistic one since it's time dependent decreasing mass due to the evaporation process. Clearly, the temperature would be time dependent as our findings. We use the semiclassical methods, namely radial null geodesic and complex paths methods. Both methods are found to give the same results. Then, we discuss the possible form of corresponding entropy.
In this paper we propose a class of embedded solutions of Einstein's field equations describing non-rotating Reissner-Nordstrom-Vaidya and rotating Kerr-Newman-Vaidya black holes.
We derive the Hawking radiation for Vaidya black hole in the tunneling picture from the corresponding single particle action by the use of the radial null geodesic and the Hamilton-Jacobi method (beyond semi-classical approximation). Both results are then analyzed and compared.
In this paper, we extend Parikh' work to the non-stationary black hole. As an example of the non-stationary black hole, we study the tunnelling effect and Hawking radiation from a Vaidya black hole whose Bondi mass is identical to its mass parameter. We view Hawking radiation as a tunnelling process across the event horizon and calculate the tunnelling probability. We find that the result is different from Parikh's work because $\frac{dr_{H}}{dv}$ is the function of Bondi mass m(v).
Hawking radiation, when treated in the ray optics limit, exhibits the unfortunate trans-Planckian problem --- a Hawking photon near spatial infinity, if back-tracked to the immediate vicinity of the horizon is hugely blue-shifted and found to have had trans-Planckian energy. (And if back-tracked all the way to the horizon, the photon is formally infinitely blue-shifted, and formally acquires infinite energy.) Unruh has forcefully argued that this implies that the Hawking flux represents a vacuum instability in the presence of a horizon, and that the Hawking photons are actually emitted from so…
We study Hawking radiation and $P-v$ criticality of charged dynamical (Vaidya) black hole in Anti-de Sitter (AdS) space. By investigating the near horizon properties of scalar field, we derive Hawking temperature of dynamical charged (Vaidya) AdS black hole. Based on this result, by regarding the cosmological constant as the thermodynamic pressure, we investigate the analogy between the charged dynamical (Vaidya) AdS black holes in the ensemble with the fixed charge and van der Waals liquid-gas system in detail, including equation of state, $P-v$ diagram, critical point, heat capacities and cr…
The Hawking radiation of Dirac particles in a charged Vaidya - de Sitter black hole is investigated by using the method of generalized tortoise coordinate transformation. It is shown that the Hawking radiation of Dirac particles does not exist for $P_1, Q_2$ components, but for $P_2, Q_1$ components it does. Both the location and the temperature of the event horizon change with time. The thermal radiation spectrum of Dirac particles is the same as that of Klein-Gordon particles.
Hawking evaporation of photons in a Vaidya-de Sitter black hole is investigated by using the method of generalized tortoise coordinate transformation. Both the location and the temperature of the event horizon depend on the time. It is shown that Hawking radiation of photons exists only for the complex Maxwell scalar $ϕ_0$ in the advanced Eddington-Finkelstein coordinate system. This asymmetry of Hawking radiation for different components of Maxwell fields probably arises from the asymmetry of spacetime in the advanced Eddington-Finkelstein coordinate system. It is shown that the black body ra…
We consider how the mass of the black hole decreases by the Hawking radiation in the Vaidya spacetime, using the concept of dynamical horizon equation, proposed by Ashtekar and Krishnan. Using the formula for the change of the dynamical horizon, we derive an equation for the mass incorporating the Hawking radiation. It is shown that final state is the Minkowski spacetime in our particular model.
In the context of a noncommutative model of coordinate coherent states, we present a Schwarzschild-like metric for a Vaidya solution instead of the standard Eddington-Finkelstein metric. This leads to the appearance of an exact $(t - r)$ dependent case of the metric. We analyze the resulting metric in three possible causal structures. In this setup, we find a zero remnant mass in the long-time limit, i.e. an instable black hole remnant. We also study the tunneling process across the quantum horizon of such a Vaidya black hole. The tunneling probability including the time-dependent part is obta…
Using the noncommutative geometry inspired Vaidya metric obtained in terms of coordinate coherent states and also utilizing the generalized uncertainty principle (GUP), we show that the nonthermal nature of the Hawking spectrum leads to Planck-scale nonthermal correlations between emitted modes of evaporation. Our analysis thus exhibits that owing to self-gravitational effects plus noncommutativity and GUP influences, information can emerge in the form of Planck-scale correlated emissions from the black hole.
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…
Hawking evaporation of Dirac particles and scalar fields in a Vaidya-type black hole is investigated by the method of generalized tortoise coordinate transformation. It is shown that Hawking radiation of Dirac particles does not exist for $P_1, Q_2$ components but for $P_2, Q_1$ components in any Vaidya-type black holes. Both the location and the temperature of the event horizon change with time. The thermal radiation spectrum of Dirac particles is the same as that of Klein-Gordon particles. We demonstrates that there is no new quantum ergosphere effect in the thermal radiation of Dirac partic…
In Vaidya-Bonner de Sitter Black hole space-time, the tunneling radiation characteristics of fermions and bosons are corrected by taking Lorentz symmetry breaking theory into account. The corresponding gamma matrices and ether-like field vectors of the black hole are constructed, then the new modified form of Dirac equation for the fermion with spin 1/2 and the new modified form of Klein-Gordon equation for boson in the curved space-time of the black hole are obtained. Through solving the two equations, new and corrected expressions of surface gravity, Hawking temperature and tunneling rate of…
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.
Hawking Radiation and Second-Order Quantum Corrected Thermodynamics with Black Hole Remnant Formation in a Vaidya-Bonnor Black Hole Surrounded by Quintessence
University of Maroua（马里瓦大学）；Higher Teachers’ Training College, University of Maroua（马里瓦大学高等师资培训学院）；University of Yaounde I（雅温得第一大学）；Ruhr-Universität Bochum（波鸿鲁尔大学）；National Advanced School of Engineering, University of Yaoundé I（雅温得第一大学国立高级工程学院）；Botswana International University of Science and Technology（博茨瓦纳科学技术大学）
We investigate the near horizon geometry of the simplest representative of the class of axisymmetric space-times: the Kerr Vaidya metrics. Kerr Vaidya metrics can be derived from the Vaidya metric by the complex coordinate transformation suggested by Newman and Janis. We show that the energy momentum tensor belongs to type 3 in the Segre Hawking Ellis classification but has a special form with all Lorentz invariant eigenvalues belonging to zero. We find a location of the apparent horizon for quasi-stationary Kerr Vaidya black holes. The energy-momentum tensor of the Kerr Vaidya geometries viol…
In the context of the semiclassical treatment of Hawking radiation we prove the universality of the reduced canonical momentum for the system of a massive shell self gravitating in a spherical gravitational field within the Painlevé family of gauges. We show that one can construct modes which are regular on the horizon both by considering as hamiltonian the exterior boundary term and by using as hamiltonian the interior boundary term. The late time expansion is given in both approaches and their time Fourier expansion computed to reproduce the self reaction 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.
The aim of this paper is to study the black hole evaporation and Hawking radiation for a noncommutative charged Vaidya black hole. For this purpose, we determine spherically symmetric charged Vaidya model and then formulate a noncommutative Reissner-Nordstr$\ddot{o}$m-like solution of this model which leads to an exact $(t-r)$ dependent metric. The behavior of temporal component of this metric and the corresponding Hawking temperature is investigated. The results are shown in the form of graphs. Further, we examine the tunneling process of the charged massive particles through the quantum hori…
The radiation rate of an evaporating black hole is calculated in a toy model in which the geometry outside the collapsing matter is described by a Vaidya metric. When back reaction consistency is imposed, the singularity in the blueshift factor near the horizon is softened, suppressing the evaporation rate in the Schwarzschild case by the fourth power of the external time, thus rendering the hole eternal.
Hawking radiation is viewed as a tunnelling process. In this way the effect of self-gravitation gives rise to semiclassical corrections to the entropy of the (2+1) BTZ black hole. The modified entropy, due to specific modelling of the self-gravitation effect, of the (2+1) BTZ black hole is evaluated. To first order in $ω$ which is a shell of energy radiated outwards the event horizon of the BTZ black hole, modified entropy is proportional to the horizon. In this semiclassical analysis, corrections to the Bekenstein-Hawking formula $S_{BH}=\mathcal{A}_{H} / 4l_{P}^{2}$ are found to be negative …
We give a detailed treatment of the back-reaction effects on the Hawking spectrum in the late-time expansion within the semiclassical approach to the Hawking radiation. We find that the boundary value problem defining the action of the modes which are regular at the horizon admits in general the presence of caustics. We show that for radii less that a certain critical value $r_c$ no caustic occurs for all values of the wave number and time and we give a rigorous lower bound on such a critical value. We solve the exact system of non linear equations defining the motion, by an iterative procedur…
Recently we showed that in semiclassical 2D dilaton gravity the regularity of a black hole horizon may be compatible with divergencies of Polyakov-Liouville stresses on it, the temperature deviating from its Hawking value. This makes the question about thermal properties of such solutions non-trivial. We demonstrate that, adding to gravitation-dilaton part of the action certain counterterms, which diverge on the horizon but are finite outside it, one may achieve finiteness of the effective gravitation-dilaton couplings on the horizon. This gives for the entropy S the Bekenstein - Hawking value…
The spectroscopy of the apparent horizon of Vaidya black holes is investigated via adiabatic invariance. We obtain an equally spaced entropy spectrum with its quantum equal to the one given by Bekenstein. We demonstrate that the quantization of entropy and area is a generic property of horizon, not only for stationary black holes, and the results also exit in a dynamical black hole. Our work also shows that the quantization of black hole is closely related to Hawking temperature, which is an interesting thing.
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Ha…
We discuss the Hawking temperature of near-equilibrium black holes using a semiclassical analysis. We introduce a useful expansion method for slowly evolving spacetime, and evaluate the Bogoliubov coefficients using the saddle point approximation. For a spacetime whose evolution is sufficiently slow, such as a black hole with slowly changing mass, we find that the temperature is determined by the surface gravity of the past horizon. As an example of applications of these results, we study the Hawking temperature of black holes with null shell accretion in asymptotically flat space and the AdS-…
Analytic semiclassical backreaction of a Schwarzschild black hole in a finite cavity: horizon shift, temperature renormalization, and canonical stability in the Hartle-Hawking State
Applying the Hamilton-Jacobi method beyond the semiclassical approximation prescribed in \cite{Majhi3} for the scalar particle, Hawking radiation as tunneling of Dirac particle through an event horizon is analysed. We show that, as before, all quantum corrections in the single particle action are proportional to the usual semiclassical contribution. We also compute the modifications to the Hawking temperature and Bekenstein-Hawking entropy for the Schwarzschild black hole. Finally, the coefficient of the logarithmic correction to entropy is shown to be related with the trace anomaly.
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 consider a gravity theory coupled to matter, where the matter has a higher-dimensional holographic dual. In such a theory, finding quantum extremal surfaces becomes equivalent to finding the RT/HRT surfaces in the higher-dimensional theory. Using this we compute the entropy of Hawking radiation and argue that it follows the Page curve, as suggested by recent computations of the entropy and entanglement wedges for old black holes. The higher-dimensional geometry connects the radiation to the black hole interior in the spirit of ER=EPR. The black hole interior then becomes part of the entangl…
Applying the Hamilton--Jacobi method we investigate the tunneling of photon across the event horizon of a static spherically symmetric black hole. The necessity of the gauge condition on the photon field, to derive the semiclassical Hawking temperature, is explicitly shown. Also, the tunneling of photon and gravitino beyond this semiclassical approximation are presented separately. Quantum corrections of the action for both cases are found to be proportional to the semiclassical contribution. Modifications to the Hawking temperature and Bekenstein-Hawking area law are thereby obtained. Using t…
The formulae for Planck length, Hawking temperature and Unruh-Davies temperature are derived by using only laws of classical physics together with the Heisenberg principle. Besides, it is shown how the Hawking relation can be deduced from the Unruh relation by means of the principle of equivalence; the deep link between Hawking effect and Unruh effect is in this way clarified.
The main topic of this talk is the Hawking effect when the black holes in question are undergoing a uniform acceleration. The semiclassical effect of the acceleration is most striking when the Hawking temperature equals the acceleration temperature. Within the usual late-time approximation, the natural black hole vacuum is then equivalent to the asymptotically empty Minkowskian vacuum, and the accelerated black hole becomes semiclassically stable against the familiar thermal evaporation. An important application of this phenomenon is found in the problem of charged black hole pair-creation.
We discuss recent work which has found, using a tunneling approach, higher-order terms in the Hawking temperature. We highlight a few important issues in the derivation, such as a misleading definition of energy, and criticize some of the conclusions that have been reached. In particular, we conclude that contrary to many recent claims, the tunneling method yields no higher-order corrections to the Hawking Temperature.
In the two-dimensional framework, the surface gravity of a (classical) black hole is independent of its mass $M$. As a consequence, the Hawking temperature and outflux are also independent of $M$ at the large-$M$ limit. (This contrasts with the four-dimensional framework, in which the surface gravity and temperature scale as 1/M.) However, when the semiclassical backreaction effects on the black-hole geometry are taken into account, the surface gravity is no longer $M$-independent, and the same applies to the Hawking temperature and outflux. This effect, which vanishes at the large-$M$ limit, …
In this paper we derive exact analytical formulas for the evolution of the photon sphere and for the angular radius of the shadow in a special Vaidya spacetime. The Vaidya metric describes a spherically symmetric object that gains or loses mass, depending on a mass function $m(v)$ that can be freely chosen. Here we consider the case that $m(v)$ is a linearly increasing or decreasing function. The first case can serve as a simple model for an accreting black hole, the second case for a (Hawking) radiating black hole. With a linear mass function the Vaidya metric admits a conformal Killing vecto…
The independent dynamical variables of a collapsing homogeneous sphere of dust are canonically quantised and coupled equations describing matter (dust) and gravitation are obtained. The conditions for the validity of the adiabatic (Born-Oppenheimer) and semiclassical approximations are derived. On neglecting back-reaction effects, it is also shown that in the vicinity of the horizon and inside the dust the Wightman function for a conformal scalar field coupled to a monopole emitter is thermal at the characteristic Hawking temperature.
Motivated by the recent work of Robinson and Wilczek, we evaluate the gravitational anomaly of a chiral scalar field in a Vaidya spacetime of arbitrary mass function, and thus the outgoing flux from the time-dependent horizon in that spacetime. We show that this flux differs from that of a perfect blackbody at a fixed temperature. When this flux is taken into account, general covariance in that spacetime is restored. We also generalize their results to the most general static, and spherically symmetric spacetime.
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…
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 show that the state of the Hawking radiation emitted from a large Schwarzschild black hole (BH) deviates significantly from a classical state, in spite of its apparent thermal nature. For this state, the occupation numbers of single modes of massless asymptotic fields, such as photons, gravitons and possibly neutrinos, are small and, as a result, their relative fluctuations are large. The occupation numbers of massive fields are much smaller and suppressed beyond even the expected Boltzmann suppression. It follows that this type of thermal state cannot be viewed as classical or even semicla…
We combine analytical and numerical techniques to study the collapse of conformally coupled massless scalar fields in semiclassical 2D dilaton gravity, with emphasis on solutions just below criticality when a black hole almost forms. We study classical information and quantum correlations. We show explicitly how recovery of information encoded in the classical initial data from the outgoing classical radiation becomes more difficult as criticality is approached. The outgoing quantum radiation consists of a positive-energy flux, which is essentially the standard Hawking radiation, followed by a…
We study the Hawking radiation in two dimensional dilaton black hole by means of quantum gravity holding near the apparent horizon. First of all, we construct the canonical formalism of the dilaton gravity in two dimensions. Then the Vaidya metric corresponding to the dilaton black hole is established where it is shown that the dilaton field takes a form of the linear dilaton. Based on the canonical formalism and the Vaidya metric, we proceed to analyze quantum properties of a dynamical black hole. It is found that the mass loss rate of the Hawking radiation is independent of the black hole ma…
We investigate the semiclassical limit and quantum corrections to the metric in a unitary quantum gravity formulation of the CGHS 2d dilaton gravity model. A new method for calculating the back-reaction effects has been introduced, as an expansion of the effective metric in powers of the matter energy-momentum tensor. In the semiclassical limit the quantum corrections can be neglected, and we show that physical states exists which contain the Hawking radiation. The first order back-reaction effect is entirely due to the Hawking radiation. It causes the black-hole mass to monotonically decrease…
Studying two-dimensional evaporating dilatonic black holes, we show that the semiclassical approximation, based on the background field approach, is valid everywhere in regions of weak curvature (including the horizon), as long as one takes into account the effects of back-reaction of the Hawking radiation on the background geometry.
Hawking showed that the radiation emitted from a classical collapsing shell is thermal. Here, we show that a semiclassical collapsing shell emits radiation that is only approximately thermal, with small but significant deviations. The most important difference is the presence of small off-diagonal elements in the radiation density matrix with a magnitude of order $1/\sqrt{S_{BH}}$, $S_{BH}$ being the Bekenstein-Hawking entropy of the incipient black hole. The off-diagonal elements store the correlations between the collapsing shell and the emitted radiation and allow information to continuousl…
