We aim to quantify the distribution of information in the Hawking radiation and inside the black hole in the semiclassical evaporation process. The structure quantum field theory forces to consider a shared information between two different regions of space-time. Using this tool, we show that the entropy of a thermal gas at the Unruh temperature underestimates the actual amount of (shared) information present in a region of the Rindler space. Then, we analyze the mutual information between the black hole and the late time radiation region. We show that in the semiclassical picture it is not possible to recover the eventual purity of the initial state in the final Hawking radiation through correlations established during the whole evaporation period, no matter the interactions present in the theory. We find extensivity of the entropy as a consequence of a reduction to a two dimensional conformal problem in a simple approximation. However, this seems not to be guaranteed in a full four dimensional calculation. We also find that a large amount of information is contained in a small approximately flat region of space-time near the point where the horizon begins. This gives place to large violations of the entropy bounds. This problem is not eased by backscattering effects and we argue that a breaking of conformal invariance is necessary to delocalize the entropy. Finally, we indicate that the mutual information could lead to a way to understand the Bekenstein-Hawking black hole entropy which does not require a reduction in degrees of freedom in order to regulate the entanglement entropy. On the contrary a large number of field degrees of freedom at high energies giving place to a Hagedorn transition implements a distance cutoff in the mutual information, which may in consequence turn out to be bounded.
Black holes of sufficiently large initial radius are expected to be well described by a semiclassical analysis at least until half of their initial mass has evaporated away. For a small number of spacetime dimensions, this holds as long as the black hole is parametrically larger than the Planck length. In that case, curvatures are small and backreaction onto geometry is expected to be well described by a time-dependent classical metric. We point out that at large $D$, small curvature is insufficient to guarantee a valid semiclassical description of black holes. Instead, the strongest bounds co…
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 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…
The formation and evaporation of small AdS black holes in a theory with a holographic dual is governed by the usual rules of quantum mechanics. The eigenstate thermalization hypothesis explains the validity of semiclassical gravity for local bulk observables and can be used to quantify the magnitude of quantum corrections to the semiclassical approximation. The holographic dual produces a basis of black hole states with finite energy width, and observables that are smooth functions on the classical phase space will self-average over a large number of energy eigenstates, exponential in the Beke…
We argue that the semiclassical analysis of the black hole information paradox is incomplete and has to be completed by an explicit entanglement of matter and quantum gravity degrees of freedom. We study in detail the evaporation process from beginning to end in the light of our extension and show that a pure initial state remains pure over the full evaporation process, including the final state which remains after the black hole has completely evaporated. By the same token we show how the quantum hair is encoded in the micro structure of the (final) gravitational state which is entangled with…
We propose a semiclassical method to calculate S-matrix elements for two-stage gravitational transitions involving matter collapse into a black hole and evaporation of the latter. The method consistently incorporates back-reaction of the collapsing and emitted quanta on the metric. We illustrate the method in several toy models describing spherical self-gravitating shells in asymptotically flat and AdS space-times. We find that electrically neutral shells reflect via the above collapse-evaporation process with probability exp(-B), where B is the Bekenstein-Hawking entropy of the intermediate b…
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 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 real time classical matrix mechanics of a simplified $2\times 2$ matrix model inspired by the black hole evaporation problem. This is a step towards making a quantitative model of real time evaporation of a black hole, which is realized as a bound state of D0-branes in string theory. The model we study is the reduction of Yang Mills in $2+1$ dimension to $0+1$ dimensions, which has been corrected with an additional potential that can be interpreted as a zero point energy for fermions. Our goal is to understand the lifetime of such a classical bound state object in the classical regime…
The pair-production process for a black hole (BH) is discussed within the framework of a recently proposed semiclassical model of BH evaporation. Our emphasis is on how the requirements of unitary evolution and strong subadditivity act to constrain the state of the produced pairs and their entanglement with the already emitted BH radiation. We find that the state of the produced pairs is indeed strongly constrained but that the semiclassical model is consistent with all requirements. We are led to the following picture: Initially, the pairs are produced in a state of nearly maximal entanglemen…
It has been observed that exact solutions for electromagnetic (EM) excitations of the Kerr-Schild (KS) geometry form outgoing beams which have very strong back reaction to metric and break the black hole horizon. As a result, interaction of a black hole with nearby electromagnetic field and electromagnetic vacuum has to cover the horizon by a set of fluctuating microholes. We integrate and analyze the Debney-Kerr-Schild equations for electromagnetic excitations of a black-hole and obtain that the exact solutions for outgoing radiation contain two related but radically different components whic…
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 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.
The evaporation of four-dimensional spherically symmetric black holes is presented in the framework of quantum field theory in curved spacetimes and semiclassical gravity. It is discussed how the evaporation process can be sourced by the presence of the trace anomaly of a massless, conformally coupled scalar field outside the apparent horizon of the black hole.
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…
Callan, Giddings, Harvey and Strominger (CGHS) previously introduced a two-dimensional semiclassical model of gravity coupled to a dilaton and to matter fields. Their model yields a system of field equations which may describe the formation of a black hole in gravitational collapse as well as its subsequent evaporation. Here we present an approximate analytical solution to the semiclassical CGHS field equations. This solution is constructed using the recently-introduced formalism of flux-conserving hyperbolic systems. We also explore the asymptotic behavior at the horizon of the evaporating bl…
We review the phenomenology of mini black holes at colliders in light of the latest data from the LHC. By improving the conventional production cross-section, we show that the current non-observation of black hole signals can be explained in terms of quantum gravity effects. In the most optimistic case, black hole production could take place at a scale slightly above the LHC design energy. We also analyse possible new signatures of quantum-corrected Planck-scale black holes: in contrast to the semiclassical scenario the emission would take place in terms of soft particles mostly on the brane.
It has been shown that the quantum state of the graviton field outside a black hole horizon carries information about the internal state of the hole. We explain how this allows unitary evaporation: the final radiation state is a complex superposition which depends linearly on the initial black hole state. Under time reversal, the radiation state evolves back to the original black hole quantum state. Formulations of the information paradox on a fixed semiclassical geometry describe only a small subset of the evaporation Hilbert space, and do not exclude overall unitarity.
We find that the end state of black hole evaporation could be represented by non-singular and without event horizon stable solitonic remnants with masses of the order the Planck scale and up to 16 units of charge. Though these objects are locally indistinguishable from spherically symmetric, massive electric (or magnetic) charges, they turn out to be sourceless geons containing a wormhole generated by the electromagnetic field. Our results are obtained by interpreting semiclassical corrections to Einstein's theory in the first-order (Palatini) formalism, which yields second-order equations and…
One-shot decoupling is a powerful primitive in quantum information theory and was hypothesized to play a role in the black hole information paradox. We study black hole dynamics modeled by a trilinear Hamiltonian whose semiclassical limit gives rise to Hawking radiation. An explicit numerical calculation of the discretized path integral of the S-matrix shows that decoupling is exact in the continuous limit, implying that quantum information is perfectly transferred from the black hole to radiation. A striking consequence of decoupling is the emergence of an output radiation entropy profile tha…
Consistency between quantum mechanical and general relativistic views of the world is a longstanding problem, which becomes particularly prominent in black hole physics. We develop a coherent picture addressing this issue by studying the quantum mechanics of an evolving black hole. After interpreting the Bekenstein-Hawking entropy as the entropy representing the degrees of freedom that are coarse-grained to obtain a semiclassical description from the microscopic theory of quantum gravity, we discuss the properties these degrees of freedom exhibit when viewed from the semiclassical standpoint. …
We investigate Hawking evaporation in a recently suggested picture in which black holes are Bose condensates of gravitons at a quantum critical point. There, evaporation of a black hole is due to two intertwined effects. Coherent excitation of a tachyonic breathing mode is responsible for the collapse of the condensate, while incoherent scattering of gravitons leads to Hawking radiation. To explore this, we consider a toy model of a single bosonic degree of freedom with derivative self-interactions. We consider the real-time evolution of a condensate and derive evaporation laws for two possibl…
