We present an analytic derivation of Hawking radiation for an arbitrary (spatial) dispersion relation $ω(k)$ as a model for ultra-high energy deviations from general covariance. It turns out that the Hawking temperature is proportional to the product of the group $dω/dk$ and phase $ω/k$ velocities evaluated at the frequency $ω$ of the outgoing radiation far away, which suggests that Hawking radiation is basically a low-energy phenomenon. Nevertheless, a group velocity growing too fast at ultra-short distances would generate Hawking radiation at ultra-high energies (``ultra-violet catastrophe'') and hence should not be a realistic model for the microscopic structure of quantum gravity.
We generalize $f(R)$-theory of anti-evaporation/evaporation for a Reissner-Nordström black hole in $n$-dimensional space-time. We consider non-linear conformally invariant Maxwell field. By perturbing the fields over Nariai-like space-time associated with degenerate horizon, we describe dynamical behavior of horizon. We show that $f(R)$-gravity can offer both anti-evaporation and evaporation in $n$-dimensional Reissner-Nordström black hole depending on the dimension $n$ and the functional form of $f(R)$. Furthermore, we argue that, in one class of non-oscillatory solution, stable and unstable …
Both the canonical and microcanonical ensembles are utilized to study the thermodynamic and evaporation properties of a closed black cosmic string whose spacetime is asymptotically anti deSitter. There are similarities and differences to the Schwarzschild-anti deSitter and 2+1 BTZ black hole solutions. It is found that there exist regimes of black string/thermal radiation equilibrium as well as stable remnant regimes. The relevance to black hole evaporation is discussed.
In the model of Expansive Nondecelerative Universe, black hole cannot totally evaporate via quantum evaporation process proposed by Hawking. In a limiting case, an equilibrium of gravitation creation and black hole evaporation can be reached keeping the surface of its horizon constant. This conclusion is in accordance with the second law of thermodynamics.
We discuss an evaporation of (2+1)-dimensional black hole by using quantum gravity holding in the vicinity of the black hole horizon. It is shown that the black hole evaporates at a definite rate by emitting matters through the quantum tunneling effect. A relation of the present formalism to the black hole entropy is briefly commented.
We derive an explicit expression for the transition amplitude from black to white hole horizon at the end of Hawking evaporation using covariant loop quantum gravity.
We apply the Generalized Uncertainty Principle (GUP) to the problem of maximum entropy and evaporation/absorption of energy of black holes near the Planck scale. We find within this general approach corrections to the maximum entropy, and indications for quenching of the evaporation because not only the evaporation term goes to a finite limit, but also because absorption of quanta seems to help the balance for black holes in a thermal bath. Then, residual masses around the Planck scale may be the final outcome of primordial black hole evaporation.
We investigate the thermodynamics of the noncommutative black hole whose static picture is similar to that of the nonsingular black hole known as the de Sitter-Schwarzschild black hole. It turns out that the final remnant of extremal black hole is a thermodynamically stable object. We describe the evaporation process of this black hole by using the noncommutativity-corrected Vaidya metric. It is found that there exists a close relationship between thermodynamic approach and evaporation process.
When a black hole evaporates, there arises a net energy flow from the black hole into its outside environment due to the Hawking radiation and the energy accretion onto black hole. Exactly speaking, due to the net energy flow, the black hole evaporation is a nonequilibrium process. To study details of evaporation process, nonequilibrium effects of the net energy flow should be taken into account. In this article we simplify the situation so that the Hawking radiation consists of non-self-interacting massless matter fields and also the energy accretion onto the black hole consists of the same f…
In Randall-Sundrum single-brane (RS-II) model, it was conjectured that there is no static large black hole localized on the brane based on adS/CFT correspondence. Here we consider the phase diagram of black objects in the models extended from the RS-II model. We propose a scenario for the phase diagram consistent with the classical black hole evaporation conjecture. The proposed scenario indicates the existence of a rich variety of the families of black objects.
The naive calculation of black hole evaporation makes the thermal emission depend on the arbitrary high frequency behaviour of the theory where the theory is certainly wrong. Using the sonic analog to black holes-- dumb holes-- I show numerically that a change in the dispersion relation at high frequencies does not seem to alter the evaporation process, lending weight to the reality of the black hole evaporation process. I also suggest a reason for the insensitivity of the process to high frequency regime.
At the end of Hawking evaporation, the horizon of a black hole enters a physical region where quantum gravity cannot be neglected. The physics of this region has not been much explored. We characterise its physics and introduce a technique to study it.
We investigate a universal behavior of thermodynamics and evaporation process for the regular black holes. We newly observe an important point where the temperature is maximum, the heat capacity is changed from negative infinity to positive infinity, and the free energy is minimum. Furthermore, this point separates the evaporation process into the early stage with negative heat capacity and the late stage with positive heat capacity. The latter represents the quantum cooling evaporation process. As a result, the whole evaporation process could be regarded as the inverse Hawking-Page phase tran…
The semi-classical back reaction to black hole evaporation (wherein the renormalized energy momentum tensor is taken as source of Einstein's equations) is analyzed in detail. It is proven that the mass of a Schwarzshild black hole decreases according to Hawking's law $dM/dt = - C/ M^2$ where $C$ is a constant of order one and that the particles are emitted with a thermal spectrum at temperature $1/8πM(t)$.
We study the evaporation of black holes in non-commutative space-times. We do this by calculating the correction to the detector's response function for a moving mirror in terms of the noncommutativity parameter $Θ$ and then extracting the number density as modified by this parameter. We find that allowing space and time to be non-commutative increases the decay rate of a black hole.
The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work I show that the causality conditions in Penrose's theorem can be almost completely removed. As a result, it is possible to infer the formation of spacetime singularities even in the absence of predictability and hence compatibly with quantum field theory and black hole evaporation.
The paper summarizes the background of Expensive Nondecelerative Universe model and its main consequences for gravitation. Applying the Vaidya metrics, the model allows for the localization and determination of the density and quantity of gravitational energy created by a body with the mass m in the distance r. The consequences are manifested both in a macrosystem (Hawking's phenomenon of black holes evaporation) and microworld phenomenon (far-infrared spectral properties)
We study the formation of a black hole and its subsequent evaporation in a model employing a minisuperspace approach to loop quantum gravity. In previous work the static solution was obtained and shown to be singularity-free. Here, we examine the more realistic dynamical case by generalizing the static case with help of the Vaidya metric. We track the formation and evolution of trapped surfaces during collapse and evaporation and examine the buildup of quantum gravitationally caused stress-energy preventing the formation of a singularity.
Usually quantum theory is formulated in terms of the evolution of states through spacelike surfaces. However, a generalization of this formulation is needed for field theory in spacetimes not foliable by spacelike surfaces, or in quantum gravity where geometry is not definite but a quantum variable. In particular, a generalization of usual quantum theory is needed for field theory in the spacetimes that model the process of black hole evaporation. This paper discusses a spacetime generalization of usual quantum theory that is applicable to evaporating black hole spacetimes. In this generalizat…
The Generalized Uncertainty Principle (GUP), motivated by current alternatives of quantum gravity, produces significant modifications to the Hawking radiation and the final stage of black hole evaporation. We show that incorporation of the GUP into the quantum tunneling process (based on the null-geodesic method) causes correlations between the tunneling probability of different modes in the black hole radiation spectrum. In this manner, the quantum information becomes encrypted in the Hawking radiation, and information can be recovered as non-thermal GUP correlations between tunneling probabi…
We investigate the dynamical formation and evaporation of a spherically symmetric charged black hole. We study the self-consistent one loop order semiclassical back-reaction problem. To this end the mass-evaporation is modeled by an expectation value of the stress-energy tensor of a neutral massless scalar field, while the charge is not radiated away. We observe the formation of an initially non extremal black hole which tends toward the extremal black hole $M=Q$, emitting Hawking radiation. If also the discharge due to the instability of vacuum to pair creation in strong electric fields occur…
We investigate the black hole thermodynamics in a "deformed" relativity framework where the energy-momentum dispersion law is Lorentz-violating and the Schwarzchild-like metric is momentum-dependent with a Planckian cut-off. We obtain net deviations of the basic thermodynamical quantities from the Hawking-Bekenstein predictions: actually, the black hole evaporation is expected to quit at a nonzero critical mass value (of the order of the Planck mass), leaving a zero temperature remnant, and avoiding a spacetime singularity. Quite surprisingly, the present semiclassical corrections to black hol…
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…
In general, when a black hole evaporates, there arises a net energy flow from black hole into its outside environment due to Hawking radiation and energy accretion onto black hole. The existence of energy flow means that the thermodynamic state of the whole system, which consists of a black hole and its environment, is in a nonequilibrium state. To know the detail of evaporation process, the nonequilibrium effects of energy flow should be taken into account. The nonequilibrium nature of black hole evaporation is a challenging topic including issues of not only black hole physics but also noneq…
We analyze the Generalized Uncertainty Principle (GUP) impact onto the nonextensive black hole thermodynamics by using Rényi entropy. We show that when introducing GUP effects, both Rényi entropy and temperature associated to black holes have finite values at the end of the evaporation process. We also study the sparsity of the radiation, associated with Rényi temperature, and compare it with the sparsity of Hawking radiation. Finally, we investigate GUP modifications to the sparsity of the radiation when GUP effects are introduced into Rényi temperature.
Understood in terms of pure states evolving into mixed states, the possibility of information loss in black holes is closely related to the global causal structure of spacetime, as is the existence of event horizons. However, black holes need not be defined by event horizons, and in fact we argue that in order to have a fully unitary evolution for black holes, they should be defined in terms of something else, such as a trapping horizon. The Misner-Sharp mass in spherical symmetry shows very simply how trapping horizons can give rise to black hole thermodynamics, Hawking radiation and singular…
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…
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…
It is widely believed that in the presence of a positive cosmological constant, heavy black holes can exhibit non-standard behaviour, namely there is a possibility that such objects would grow instead of evaporating. We point out that all those results (obtained in different frameworks) rely heavily upon the identification of the Nariai spacetime with the Schwarzschild--de Sitter (Kottler) black hole. In this note we argue that it is an incorrect assumption. As a result, previous treatments need revisiting. In particular, we show that within effective action approach, there is no solution corr…
We study the consequences of nonzero neutrino masses for black holes evaporating by the emission of Hawking radiation. We find that the evolution of small, hot, black holes may be unaffected (if neutrinos are Majorana particles), or may show an increase in neutrino luminosity and a decrease in lifetime by up to a factor of 1.85 (if neutrinos are Dirac particles). However, for sufficiently large (e.g., stellar mass) black holes, neutrino emission is largely or entirely suppressed, resulting in a decrease in emitted power and an increase in lifetime by up to a factor of 7.5.
We extend the recently proposed Black Hole Entropy Distance Conjecture to the case of charged black holes in de Sitter space. By systematically studying distances in the space of black hole geometries with multiple horizons, we find that the distance is generically related to the logarithm of the entropy. From the infinite distance conjecture this predicts the appearance of a massless tower of modes in the limit of infinite entropy. Further, we study the evaporation of these black holes and relate it to the geometric distance. We find that the corresponding distance to the final stage of evapo…
Primordial black holes with a narrow mass range are regarded as a nonrelativistic fluid component with an equation of state for dust. The impact of the black hole evaporation on the dynamics of the early universe is studied by resorting to a two-fluid model. We find periods of intense radiation reheating in the initial and final stages of the evaporation.
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…
We present the public code \texttt{BlackHawk}, a powerful tool to compute the evaporation of any distribution of Schwarzschild and Kerr Black Holes and the emission spectra of Hawking radiation.
A model is proposed to describe a transition from a Schwarzschild black hole of mass $M_{0}$ to a Schwarzschild black hole of mass $M_{1}$ $\leq M_{0}$. The basic equations are derived from the non-vacuum Einstein field equations taking a source representing a null scalar field with a nonvanishing trace anomaly. It is shown that the nonvanishing trace anomaly of the scalar field prevents a complete evaporation.
We show within the usual two-dimensional approximation that unitarity and the restoration of Minkowski vacuum correlations at the end of black hole evaporation impose unexpected constraints on its mass loss rate: before disappearing the black hole emits one or more negative energy burst, leading to a temporary increase of its mass.
This paper shows a way of how one may resolve the non-unitarity problem in black-hole physics without modifications of the basic principles of local quantum field theory.
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 study the influence of black-hole evaporation on light propagation. The framework employed is based on the non-linear QED effective action at one-loop level. We show that the light-cone condition is modified for low-energy radiation due to black-hole evaporation. We discuss conditions under which the phase velocity of this low-energy radiation is greater than $c$. We also compute the modified light-deflection angle, which turns out to be significantly different from the standard GR value for black-hole masses in the range $M_\text{Pl} \ll M \lesssim 10^{19}\;M_\text{Pl}$.
We discuss dyonic black hole solutions in the case of $f(R)$-gravity coupled with a dilaton and two gauge bosons. The study of such a model is highly motivated from string theory. Our Black Hole solutions are extensions of the one firstly studied by Kallosh, Linde, Ortín, Peet and Van Proyen (KLOPV) in [arXiv:hep-th/9205027]. We will show that extreme solutions are unstable. In particular, these solutions have Bousso-Hawking-Nojiri-Odintsov (anti)evaporation instabilities.
First we have assumed the most general static spherically symmetric black hole metric. The accretion of any general kind of fluid flow around the black hole have been investigated. The accretion of fluid flow around the modified Hayward black hole have been analyzed and we then calculated the critical point, fluid 4 velocity and velocity of sound during accretion process. Also the nature of the dynamical mass of black hole during accretion of fluid flow and taking into consideration of Hawking radiation from black hole i.e., evaporation of black hole have been analyzed.
We analyze how a quantum-gravity-induced change in the number of thermal dimensions (through a modified dispersion relation) affects the geometry and the thermodynamics of a charged black hole. To that end we resort to Kiselev's solution as the impact such modifications have on the evaporation rate of the black hole becomes more clear. As an application, we study the case for which the thermal dimension is reduced to two.
Black hole evaporation may lead to massive or massless remnants, or naked singularities. This paper investigates this process in the context of two quite different two dimensional black hole models. The first is the original CGHS model, the second is another two dimensional dilaton-gravity model, but with properties much closer to physics in the real, four dimensional, world. Numerical simulations are performed of the formation and subsequent evaporation of black holes and the results are found to agree qualitatively with the exactly solved modified CGHS models, namely that the semiclassical a…
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…
The formation of near-extremal Reissner-Nordstrom black holes in the S-wave approximation can be described, near the event horizon, by an effective solvable model. The corresponding one-loop quantum theory remains solvable and allows to follow analytically the evaporation process which is shown to require an infinite amount of time.
We study the stability under the perturbation and the related anti-evaporation of the Nariai space-time in bigravity. If we impose specific condition for the solutions and parameters, we obtain asymptotically de Sitter space-time, and show the existence of the Nariai space-time as a background solution. Considering the perturbation around the Nariai space-time up to first order, we investigate the behavior of black hole horizon. We show that the anti-evaporation does not occur on the classical level in the bigravity.
We review (anti)evaporation phenomena within the context of quantum gravity and extended theories of gravity. The (anti)evaporation effect is an instability of the black hole horizon discovered in many different scenarios: quantum dilaton-gravity, $f(R)$-gravity, $f(T)$-gravity, string inspired black holes and brane-world cosmology. Evaporating and antievaporating black holes seem to have completely different thermodynamical features compared to standard semiclassical black holes. The purpose of this review is to provide an introduction to conceptual and technical aspects of (anti)evaporation …
We consider the black hole information problem in an explicitly defined spacetime modelling black hole evaporation. Using this context we review basic aspects of the problem, with a particular effort to be unambiguous about subtle topics, for instance precisely what is meant by entropy in various circumstances. We then focus on questions of unitarity, and argue that commonly invoked semiclassical statements of long term, evaporation time, and Page time "unitarity" may all be violated even if physics is fundamentally unitary. This suggests that there is no horizon firewall. We discuss how the p…
We discuss the relevance of quantum gravitational corrections to the functional Schrödinger equation for the information loss paradox in black hole evaporation. These corrections are found from the Wheeler-DeWitt equation through a semiclassical expansion scheme. The dominant contribution in the final evaporation stage, when the black hole approaches the Planck regime, is a term which explicitly violates unitarity in the non-gravitational sector. While pure states remain pure, there is an increase in the degree of purity for non-pure states in this sector. This result holds irrespective of whe…
Black hole formation/evaporation in two-dimensional dilaton gravity can be described, in the limit where the number $N$ of matter fields becomes large, by a set of second-order partial differential equations. In this paper we solve these equations numerically. It is shown that, contrary to some previous suggestions, black holes evaporate completely a finite time after formation. A boundary condition is required to evolve the system beyond the naked singularity at the evaporation endpoint. It is argued that this may be naturally chosen so as to restore the system to the vacuum. The analysis als…
For the radial motion of massive particles with large angular momenta in Schwarzschild geometry and that of massive charged particles with large angular momenta or energy in a particular range in Reissner--Nordström geometry, there exist classically forbidden regions on the outside of the respective event horizons which scatter certain infalling geodesics or screen some of the black holes' evaporation by reflecting the emitted particles back into the black holes. Quantum tunneling across this forbidden regions is studied.
