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 probabilities of different modes.
We discuss the evaporation and antievaporation instabilities of Nariai solution in extended theories of gravity. These phenomena were explicitly shown in several different extensions of General Relativity, suggesting that a universal cause is behind them. We show that evaporation and antievaporation are originated from deformations of energy conditions on the Nariai horizon. Energy conditions get new contributions from the extra propagating degrees of freedom, which can provide extra focalizing or antifocalizing terms in the Raychanduri equation. We also show two explicit examples in $f(R)$-gr…
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.
Positive energy singularities induced by Sine-Gordon solitons in 1+1 dimensional dilaton gravity with positive and negative cosmological constant are considered. When the cosmological constant is positive, the singularities combine a white hole, a timelike singularity and a black hole joined smoothly near the soliton center. When the cosmological constant is negative, the solutions describe two timelike singularities joined smoothly near the soliton center. We describe these spacetimes and examine their evaporation in the one loop approximation.
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.
Black holes in $d < 3$ spatial dimensions are studied from the perspective of the corpuscular model of gravitation, in which black holes are described as Bose-Einstein condensates of (virtual soft) gravitons. In particular, since the energy of these gravitons should increase as the black hole evaporates, eventually approaching the Planck scale, the lower dimensional cases could provide important insight into the late stages and end of Hawking evaporation. We show that the occupation number of gravitons in the condensate scales holographically in all dimensions as $N_d \sim \left(L_d/\ell_{\rm …
The issue of unitary evolution during creation and evaporation of a black hole remains controversial. We~argue that some prominent cures are more troubling than the disease, demonstrate that their central element---forming of the event horizon before the evaporation begins---is not necessarily true, and describe a fully coupled matter-gravity system which is manifestly unitary.
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 study the problem of a four-dimensional brane lying in the five-dimensional degenerate Schwarzschild-de Sitter (Nariai) black hole, in five-dimensional $F(R)$-gravity. We show that there cannot exist the brane in the Nariai bulk space except the case that the brane tension vanishes. We demonstrate that the five-dimensional Nariai bulk is unstable in a large region of the parameter space. In particular, the Nariai bulk can have classical (anti-)evaporation instabilities. The bulk instability back-reacts on the four-dimensional brane, in case that the brane tension vanishes, and the unstable …
A semiclassical two-dimensional dilaton-gravity model is obtained by dimensional reduction of the spherically symmetric five-dimensional Einstein equations and used to investigate black hole evaporation. It is shown that this model prevents the formation of naked singularity and allows spacetime wormholes to contribute the process of formation and evaporation of black holes.
We describe a classical configuration of conformal matter forming a naked singularity and discuss its subsequent Hawking evaporation within the context of two dimensional dilaton gravity. The one loop analysis is credible for a large mass naked singularity and suggests the existence of a weak cosmological censorship that would cause it to explode into radiation upon forming. (Hardcopies of figures available on request)
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.
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 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 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…
A possible resolution of the information loss paradox for black holes is proposed in which a phase transition occurs when the temperature of an evaporating black hole equals a critical value, $T_c$, and Lorentz invariance and diffeomorphism invariance are spontaneously broken. This allows a generalization of Schrödinger's equation for the quantum mechanical density matrix, such that a pure state can evolve into a mixed state, because in the symmetry broken phase the conservation of energy-momentum is spontaneously violated. TCP invariance is also spontaneously broken together with time reversa…
We studied the anti-evaporation of degenerate Schwarzschild-de Sitter black hole (so-called Nariai space-time) in modified $F(R)$ gravity. The analysis of perturbations of the Nariai black hole is done with the conclusion that anti-evaporation may occur in such a theory already on classical level. For several power-law $F(R)$ gravities which may describe the inflation and/or dark energy eras we presented the theory parameters bounds for occurrence of anti-evaporation and conjectured creation of infinite number of horizons.
In this work, we explore all possible scenarios in the evaporation process of a spherical neutral AdS black hole in four-dimensional conformal gravity, where the equations of states are branched. In one branch, the final states correspond to the extremal black hole where the total decay time is divergent given any initial mass. In the other branch, the black holes always evaporate completely with in a finite time; the total decay time depends linearly on the AdS radius, when the mass is taken to be infinity.
We study the instabilities and related anti-evaporation of the extremal Reissner-Nordström (RN) black hole in $F(R)$ gravity. It is remarkable that the effective electric charge can be generated for some solutions of $F(R)$ gravity without electromagnetic field. The anti-evaporation effect occurs but it emerges only in the strong coupling limit of the effective gravitational coupling. The instabilities of RN black hole are also investigated when the electromagnetic sector is added to the action of $F(R)$ gravity. We show the anti-evaporation occurs in the Maxwell-$F(R)$ gravity with the arbitr…
The understanding of black holes in loop quantum gravity is becoming increasingly accurate. This review focuses on the possible experimental or observational consequences of the underlying spinfoam structure of space-time. It adresses both the aspects associated with the Hawking evaporation and the ones due to the possible existence of a bounce. Finally, consequences for dark matter and gravitational waves are considered.
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…
The original derivation of Hawking radiation shows the complete evaporation of black holes. However, theories of quantum gravity predict the existence of the minimal observable length. In this paper, we investigate the tunneling radiation of the scalar particles by introducing quantum gravity effects influenced by the generalized uncertainty principle. The Hawking temperatures are not only determined by the properties of the black holes, but also affected by the quantum numbers of the emitted particles. The quantum gravity corrections slow down the increase of the temperatures. The remnants ar…
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 the future evolution of Nariai black hole which is extremal limit of Schwarzschild-de Sitter one in modified gravity. The perturbations equations around Nariai black hole are derived in static and cosmological patches for general $F(R)$-gravity. The analytical and numerical study of several realistic $F(R)$-models shows the occurence of rich variety of scenarios: instabilities, celebrated Hawking evaporation and anti-evaporation of black hole. The realization of specific scenario depends on the model under consideration. It is remarkable that the presence of such primordial blac…
Extending previous work on the formation and the evaporation of black holes in conformal gravity, in the present paper we study the gravitational collapse of a spherically symmetric and electrically charged thin shell of radiation. The process creates a singularity-free black hole. Assuming that in the evaporation process the charge $Q$ is constant, the final product of the evaporation is an extremal remnant with $M=Q$, which is reached in an infinite amount of time. We also discuss the issue of singularity and thermodynamics of black holes in Weyl's conformal 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 …
Hořava-Lifshitz (HL) gravity was formulated in hope of solving the non-renormalization problem in Einstein gravity and the ghost problem in higher derivative gravity theories by violating Lorentz invariance. In this work we consider the spherically symmetric neutral AdS black hole evaporation process in HL gravity in various spacetime dimensions $d$, and with detailed balance violation parameter $0\leqslant ε^2\leqslant 1$. We find that the lifetime of the black holes under Hawking evaporation is dimensional dependent, with $d=4,5$ behave differently from $d\geqslant 6$. For the case of $ε=0$,…
Extremal cosmological black holes are analysed in the framework of the most general second order scalar-tensor theory, the~so-called Horndeski gravity. Such~extremal black holes are a particular case of Schwarzschild-De Sitter black holes that arises when the black hole horizon and the cosmological one coincide. Such~metric is induced by a particular value of the effective cosmological constant and is known as Nariai spacetime. The~existence of this type of solutions is studied when considering the Horndeski Lagrangian and its stability is analysed, where the so-called anti-evaporation regime …
We point out that two-dimensional Russo-Susskind-Thorlacius (RST) model for evaporating black holes is locally equivalent - at the full quantum level - to flat-space Jackiw-Teitelboim (JT) gravity that was recently shown to be unitary. Globally, the two models differ by a reflective spacetime boundary added in the RST model. Treating the boundary as a local and covariant deformation of quantum JT theory, we develop sensible semiclassical description of evaporating RST black holes. Nevertheless, our semiclassical solutions fail to resolve the information recovery problem, and they do not indica…
We revisit the hypothesis of a possible line structure in the Hawking evaporation spectrum of black holes. Because of nonperturbative quantum gravity effects, this would take place arbitrarily far away from the Planck mass. We show, based on a speculative but consistent hypothesis, that this naive prediction might in fact hold in the specific context of loop quantum gravity. A small departure from the ideal case is expected for some low-spin transitions and could allow us to distinguish several quantum gravity models. We also show that the effect is not washed out by the dynamics of the proces…
Quantum gravity correction is truly important to study tunnelling process of black hole. Base on the generalized uncertainty principle, we investigate the influence of quantum gravity and the result tell us that the quantum gravity correction accelerates the evaporation of black hole. Using corrected Dirac equation in curved spacetime and Hamilton-Jacobi method, we address the tunnelling of fermions in a 4-dimensional Schwarzschild spacetime. After solving the equation of motion of the spin 1/2 field, we obtain the corrected Hawking temperature. It turns out that the correction depends not onl…
Spin effects on particle creation and evaporation in $f(R,T)$ gravity
Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）；Khazar University（哈扎尔大学）；Damghan University（达姆甘大学）；Universidade de Lisboa（里斯本大学）
We provide general arguments regarding the connection between low-energy theories (gravity and quantum field theory) and a hypothetical fundamental theory of quantum gravity, under the assumptions of (i) validity of the holographic bound and (ii) preservation of unitary evolution at the level of the fundamental theory. In particular, the appeal to the holographic bound imposed on generic physical systems by the Bekenstein-Hawking entropy implies that both classical geometry and quantum fields propagating on it should be regarded as phenomena emergent from the dynamics of the fundamental theory…
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.
We study the formation and the evaporation of a spherically symmetric black hole in conformal gravity. From the collapse of a spherically symmetric thin shell of radiation, we find a singularity-free non-rotating black hole. This black hole has the same Hawking temperature as a Schwarzschild black hole with the same mass, and it completely evaporates either in a finite or in an infinite time, depending on the ensemble. We consider the analysis both in the canonical and in the micro-canonical statistical ensembles. Last, we discuss the corresponding Penrose diagram of this physical process.
We investigate the black hole evaporation process in Lovelock gravity with diverse dimensions. By selecting the appropriate coefficients, the space-time solutions can possess a unique AdS vacuum with a fixed cosmological constant $Λ=-\frac{(d-1)(d-2)}{2\ell^{2}}$. The black hole solutions can be divided into two cases: $d>2k+1$ and $d=2k+1$. In the case of $d>2k+1$, the black hole is in an analogy with the Schwarzschild AdS black hole, and the life time is bounded by a time of the order of $\ell^{d-2k+1}$, which reduces Page's result on the Einstein gravity in $k=1$. In the case of $d=2k+1$, t…
A personal perspective on the black hole evaporation process is presented using as guidelines inputs from: (i) loop quantum gravity, (ii) simplified models where concrete results have been obtained, and, (iii) semi-classical quantum general relativity. On the one hand, the final picture is conservative in that there are concrete results that support each stage of the argument, and there are no large departures from general relativity or semi-classical gravity in tame regions outside macroscopic black holes. On the other hand it argues against certain views that are commonly held in many quarte…
In earlier Letters, we adopted a complex approach to quantum processes in the formation and evaporation of black holes. Taking Feynman's $+iε$ prescription, rather than than one of the more usual approaches, we calculated the quantum amplitude (not just the probability density) for final weak-field configurations following gravitational collapse to a black hole with subsequent evaporation. What we have done is to find quantum amplitudes relating to a pure state at late times following black-hole matter collapse. Such pure states are then shown to be susceptible to a description in terms of coh…
A theory of quantum gravity is expected to change profoundly our understanding of black holes. Quantum theory has already shown, as a first approximation, that a black hole slowly evaporates. Non-perturbative quantum gravity also predicts that such an object could metamorphose into a white hole, its time-reverse. In this thesis, we study the foundations of such a scenario and propose a mathematical model that includes the phenomenon of evaporation.
This paper provides an extension for Hawking temperature of Reissner-Nordstr$\ddot{o}$m-de Sitter (RN-DS) black hole (BH) with global monopole as well as $5$D charged black hole. We consider the black holes metric and investigate the effects of quantum gravity ($α$) on Hawking radiation. We investigate the charged boson particles tunneling through the horizon of black holes by using the Hamilton-Jacobi ansatz phenomenon. In our investigation, we study the quantum radiation to analyze the Lagrangian wave equation with generalized uncertainty principle and calculate the modified Hawking temperat…
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.
Thermodynamics and information recovery of Schwarzschild AdS black holes in conformal Killing gravity
Mohammed I University（穆罕默德一世大学）；Astrophysical and Cosmological Center（天体物理与宇宙学中心）；Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa（里斯本大学科学学院天体物理学与空间科学研究所）；Departamento de Física, Faculdade de Ciências da Universidade de Lisboa（里斯本大学科学学院物理系）
Verlinde recently suggested that gravity, inertia, and even spacetime may be emergent properties of an underlying thermodynamic theory. This vision was motivated in part by Jacobson's 1995 surprise result that the Einstein equations of gravity follow from the thermodynamic properties of event horizons. Taking a first tentative step in such a program, we derive the evaporation rate (or radiation spectrum) from black hole event horizons in a spacetime-free manner. Our result relies on a Hilbert space description of black hole evaporation, symmetries therein which follow from the inherent high di…
In this work we analyse the backreaction of a quantum field on a spherically symmetric black hole geometry with an inner horizon, i.e. an internal boundary of the trapped region. We start with a black hole background with an inner horizon which remains static after its formation. We quantise a massless scalar field on it and calculate its renormalised stress-energy tensor in the Polyakov approximation. We use this tensor as a source of perturbation on top of the background spacetime. We find that the inner horizon has a tendency to evaporate outward much more quickly than the outer one evapora…
We describe the black hole evaporation process driven by the dynamical evolution of the quantum gravitational degrees of freedom resident at the horizon, as identified by the loop quantum gravity kinematics. Using a parallel with the Brownian motion, we interpret the first law of quantum dynamical horizon in terms of a fluctuation-dissipation relation. In this way, the horizon evolution is described in terms of relaxation to an equilibrium state balanced by the excitation of Planck scale constituents of the horizon. This discrete quantum hair structure associated to the horizon geometry produc…
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…
During the final stages of black hole evaporation, ultraviolet deviations from General Relativity eventually become dramatic, potentially affecting the end-state. We explore this problem by performing nonlinear simulations of wave packets in Einstein-dilaton-Gauss-Bonnet gravity, the only gravity theory with quadratic curvature terms which can be studied at fully nonperturbative level. Black holes in this theory have a minimum mass but also a nonvanishing temperature. This poses a puzzle concerning the final fate of Hawking evaporation in the presence of high-curvature nonperturbative effects.…
A paradigm describing black hole evaporation in non-perturbative quantum gravity is developed by combining two sets of detailed results: i) resolution of the Schwarzschild singularity using quantum geometry methods; and ii) time-evolution of black holes in the trapping and dynamical horizon frameworks. Quantum geometry effects introduce a major modification in the traditional space-time diagram of black hole evaporation, providing a possible mechanism for recovery of information that is classically lost in the process of black hole formation. The paradigm is developed directly in the Lorentzia…
