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 picture is modified for regular (nonsingular) evaporation models. We also compare our conclusions to recent holographic studies, and argue that they are mutually compatible.
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…
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 explore the Hawking evaporation of two-dimensional anti-de Sitter (AdS$_2$), dilatonic black hole coupled with conformal matter, and derive the Page curve for the entanglement entropy of radiation. We first work in a semiclassical approximation with backreaction. We show that the end-point of the evaporation process is AdS$_2$ with a vanishing dilaton, i.e. a regular, singularity-free, zero-entropy state. We explicitly compute the entanglement entropies of the black hole and the radiation, as functions of the horizon radius, using the conformal field theory (CFT) dual to AdS$_2$ gravity. We…
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.
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.
We construct the propagator of a non-relativistic non-interacting particle in a flat spacetime in which two regions have been identified. This corresponds to the simplest "time machine". We show that while completeness is lost in the vicinity of the time machine it holds before the time machine appears and it is recovered afterwards. Unitarity, however, is not satisfied anywhere. We discuss the implications of these results and their relationship to the loss of unitarity in black hole evaporation.
Unitary black hole evaporation necessarily involves a late-time superposition of decoherent states, including states describing distinct spacetimes (e.g., different center of mass trajectories of the black hole). Typical analyses of the black hole information problem, including the argument for the existence of firewalls, assume approximate unitarity ("factorization of unitarity") on each of the decoherent spacetimes. This factorization assumption is non-trivial, and indeed may be incorrect. We describe an ansatz for the radiation state that violates factorization and which allows unitarity an…
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…
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…
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 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 …
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.
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.
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…
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…
We discuss the black hole information problem, including the recent claim that unitarity requires a horizon firewall, emphasizing the role of decoherence and macroscopic superpositions. We consider the formation and evaporation of a large black hole as a quantum amplitude, and note that during intermediate stages (e.g., after the Page time), the amplitude is a superposition of macroscopically distinct (and decohered) spacetimes, with the black hole itself in different positions on different branches. Small but semiclassical observers (who are themselves part of the quantum amplitude) that fall…
We discuss the near singularity region of the linear mass Vaidya metric for massless particles with non-zero angular momentum. In particular we look at massless geodesics with non-zero angular momentum near the vanishing point of a special subclass of linear mass Vaidya metrics. We also investigate this same structure in the numerical solutions for the scattering of massless scalars from the singularity. Finally we make some comments on the possibility of using this metric as a semi-classical model for the end-point of black hole evaporation.
We discuss how in certain theories of spacetime admitting a maximal proper acceleration Hawking radiation does not completely evaporate the black hole. The black hole remnant's mass depends on the inverse of the maximal acceleration. Furthermore, as a consequence of a duality between the minimum mass that a Schwarzschild black hole can have in such spacetimes and the maximal acceleration, we show that in certain theories with a maximal acceleration there must be an upper uniform bounds on the value of the force that can be exerted on test particles.
We examine the evaporation of two--dimensional black holes, the classical space--times of which are extended geometries, like for example the two--dimensional section of the extremal Reissner--Nordstrom black hole. We find that the evaporation in two particular models proceeds to a stable end--point. This should represent the generic behavior of a certain class of two--dimensional dilaton--gravity models. There are two distinct regimes depending on whether the back--reaction is weak or strong in a certain sense. When the back--reaction is weak, evaporation proceeds via an adiabatic evolution, …
We construct a dilatonic two-dimensional model of a charged black hole. The classical solution is a static charged black hole, characterized by two parameters, $m$ and $q$, representing the black hole's mass and charge. Then we study the semiclassical effects, and calculate the evaporation rate of both $m$ and $q$, as a function of these two quantities. Analyzing this dynamical system, we find two qualitatively different regimes, depending on the electromagnetic coupling constant $g_{A}$. If the latter is greater than a certain critical value, the charge-to-mass ratio decays to zero upon evapo…
These lecture notes are an elementary and pedagogical introduction to the black hole evaporation, based on a lecture given by the author at the Ninth Modave Summer School in Mathematical Physics and are intended for PhD students. First, quantum field theory in curved spacetime is studied and tools needed for the remaining of the course are introduced. Then, quantum field theory in Rindler spacetime in 1+1 dimensions and in the spacetime of a spherically collapsing star are considered, leading to Unruh and Hawking effects, respectively. Finally, some consequences such as thermodynamics of black…
We study the evaporation of black holes in space-times with extra dimensions of size L. We first obtain a potential which describes the expected behaviors of very large and very small black holes and then show that a (first order) phase transition, possibly signaled by an outburst of energy, occurs in the system when the horizon shrinks below L from a larger value. This is related to both a change in the topology of the horizon and the restoring of the translational symmetry along the extra dimensions.
We numerically analyze the evolution of a two-dimensional dilatonic black hole, within the CGHS model. We focus our attention on the finite-mass corrections to the universal evaporation rate which applies at the large-mass limit. Our numerical results confirm a previous theoretical prediction for the first-order ($\propto 1/M$) correction. In addition, our results strongly suggest that the next-order ($\propto 1/M^{2}$) term vanishes, and provide a rough estimate for the third-order term.
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.
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 consider Hawking radiation as due to a tunneling process in a black hole were quantum corrections, derived from Quantum Einstein Gravity, are taken into account. The consequent derivation, satisfying conservation laws, leads to a deviation from an exact thermal spectrum. The non-thermal radiation is shown to carry information out of the black hole. Under the appropriate approximation, a quantum corrected temperature is assigned to the black hole. The evolution of the quantum black hole as it evaporates is then described by taking into account the full implications of energy conservation as …
Hawking has proposed non-unitary rules for computing the probabilistic outcome of black hole formation. It is shown that the usual interpretation of these rules violates the superposition principle and energy conservation. Refinements of Hawking's rules are found which restore both the superposition principle and energy conservation, but leave completely unaltered Hawking's prediction of a thermal emission spectrum prior to the endpoint of black hole evaporation. These new rules violate clustering. They further imply the existence of superselection sectors, within each of which clustering is r…
A new simple qubit model of black hole evaporation is proposed. The model operates on four qubits and is defined in terms of quantum gates and a quantum circuit. The chief features of the model include explicit unitarity and (most notably) causality which is understood as the impossibility of the transfer of information from the interior of the black hole through its horizon. The corresponding von Neumann entanglement entropy yields a crude (four-qubit) approximation of the Page curve.
The formation and evaporation of a black hole can be viewed as a scattering process in Quantum Gravity. Semiclassical arguments indicate that the process should be non-unitary, and that all the information of the original quantum state forming the black hole should be lost after the black hole has completely evaporated, except for its mass, charge and angular momentum. This would imply a violation of basic principles of quantum mechanics. We review some proposed resolutions to the problem, including developments in string theory and a recent proposal by Hawking. We also suggest a novel approac…
Regular (non-singular) space-times are given which describe the formation of a (locally defined) black hole from an initial vacuum region, its quiescence as a static region, and its subsequent evaporation to a vacuum region. The static region is Bardeen-like, supported by finite density and pressures, vanishing rapidly at large radius and behaving as a cosmological constant at small radius. The dynamic regions are Vaidya-like, with ingoing radiation of positive energy flux during collapse and negative energy flux during evaporation, the latter balanced by outgoing radiation of positive energy …
We construct a one-loop effective metric describing the evaporation phase of a Schwarzschild black hole in a spherically symmetric null-dust model. This is achieved by quantising the Vaidya solution and by chosing a time dependent quantum state. This state describes a black hole which is initially in thermal equilibrium and then the equilibrium is switched off, so that the black hole starts to evaporate, shrinking to a zero radius in a finite proper time. The naked singularity appears, and the Hawking flux diverges at the end-point. However, a static metric can be imposed in the future of the …
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 $ε=0$,…
On Radiative Fluxes and Coulombic Charges in the Balance Law for Black Hole Evaporation
The Pennsylvania State University（宾夕法尼亚州立大学）；Department of Physics, The Pennsylvania State University（物理学系，宾夕法尼亚州立大学）；Applied Research Lab, The Pennsylvania State University（应用研究实验室，宾夕法尼亚州立大学）
We analyze Hawking evaporation of the Callen-Giddings-Harvey-Strominger (CGHS) black holes from a quantum geometry perspective and show that information is not lost, primarily because the quantum space-time is sufficiently larger than the classical. Using suitable approximations to extract physics from quantum space-times we establish that: i)future null infinity of the quantum space-time is sufficiently long for the the past vacuum to evolve to a pure state in the future; ii) this state has a finite norm in the future Fock space; and iii) all the information comes out at future infinity; ther…
We study the effect of back-reaction on the evaporation of quantum black holes. The method used is based on quantum tunneling formalism as proposed in [4]. We give a more realistic picture by considering the fact that a black hole looses its energy while modes are tunneled outside the event horizon. It is shown how the tunneling quantum field modes affect the geometry and how this change in geometry is arrested in the quantum field. Exploiting this we calculate the modified (nonthermal) radiation spectrum, associating energy fluxes and discuss various issues related with these. The results obt…
In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any effective smooth field theoretical description would miss part of the fundamental degrees of freedom and thus break unitarity. This is applicable also to trivial gravitational field (low energy) idealizations realized by the use of the Minkowski background geometry which, as any other spacetime geometry, corresponds, in the fundamental description, to infinitely many different and closely degenerate discrete microstates. The existence of such microstates prov…
Constructing an exact correspondence between a black hole model, formed from the most simple solution of Einstein's equations, and a particular moving mirror trajectory, we investigate a new model that preserves unitarity. The Bogoliubov coefficients in 1+1 dimensions are computed analytically. The key modification limits the origin of coordinates (moving mirror) to sub-light asymptotic speed. Effective continuity across the metric ensures that there is no information loss. The black hole emits thermal radiation and the total evaporation energy emitted is finite without backreaction, consisten…
