# Information loss problem and a `black hole' model with a closed apparent horizon

TL;DR: In this article, a modified Vaidya metric is proposed to describe the evaporation process of a black hole, where the curvature is limited by some value (of the order of the Planckian one).

Abstract: In a classical description the spacetime curvature inside a black hole infinitely grows. In the domain where it reaches the Planckian value and exceeds it the Einstein equations should be modified. In the absence of reliable theory of quantum gravity it is instructive to consider simplified models. We assume that a spacetime curvature is limited by some value (of the order of the Planckian one). We use modified Vaidya metric, proposed by Hayward, to describe the black hole evaporation process. In such a spacetime the curvature near $r=0$ remains finite, it does not have an event horizon and its apparent horizon is closed. If the initial mass of such a `black hole' is much larger than the Planckian one its properties (as seen by an external observer) are practically the same as properties of the `standard' black hole with the event horizon. We study outgoing null rays in the vicinity of the outer apparent and introduce a notion of quasi-horizon. We demonstrate that particles, trapped inside a `black hole' during the evaporation process, finally may return to external space after the evaporation is completed. We also demonstrate that such quanta would have very large blue-shift. The absence of the event horizon makes it possible restoration of the unitarity in evaporating black holes.

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TL;DR: In this paper, the authors consider static spherically symmetric metrics which represent nonsingular black holes in four-and higher-dimensional spacetime and show that such a metric cannot describe a non-singular black hole.

Abstract: We discuss static spherically symmetric metrics which represent nonsingular black holes in four- and higher-dimensional spacetime. We impose a set of restrictions, such as a regularity of the metric at the center $r=0$ and Schwarzschild asymptotic behavior at large $r$. We assume that the metric besides mass $M$ contains an additional parameter $\ensuremath{\ell}$, which determines the scale where modification of the solution of the Einstein equations becomes significant. We require that the modified metric obeys the limiting curvature condition; that is, its curvature is uniformly restricted by the value $\ensuremath{\sim}{\ensuremath{\ell}}^{\ensuremath{-}2}$. We also make a ``more technical'' assumption that the metric coefficients are rational functions of $r$. In particular, the invariant $(\ensuremath{
abla}r{)}^{2}$ has the form ${P}_{n}(r)/{\stackrel{\texttildelow{}}{P}}_{n}(r)$, where ${P}_{n}$ and ${\stackrel{\texttildelow{}}{P}}_{n}$ are polynomials of the order of $n$. We discuss first the case of four dimensions. We show that when $n\ensuremath{\le}2$ such a metric cannot describe a nonsingular black hole. For $n=3$ we find a suitable metric, which besides $M$ and $\ensuremath{\ell}$ contains a dimensionless numerical parameter. When this parameter vanishes, the obtained metric coincides with Hayward's one. The characteristic property of such spacetimes is $\ensuremath{-}{\ensuremath{\xi}}^{2}=(\ensuremath{
abla}r{)}^{2}$, where ${\ensuremath{\xi}}^{2}$ is a timelike at infinity Killing vector. We describe a possible generalization of a nonsingular black-hole metric to the case when this equality is violated. We also obtain a metric for a charged nonsingular black hole obeying similar restrictions as the neutral one and construct higher dimensional models of neutral and charged black holes.

232 citations

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TL;DR: In this article, it was shown that there is a classical metric satisfying the Einstein equations outside a finite spacetime region where matter collapses into a black hole and then emerges from a white hole.

Abstract: We show that there is a classical metric satisfying the Einstein equations outside a finite spacetime region where matter collapses into a black hole and then emerges from a white hole. We compute this metric explicitly. We show how quantum theory determines the (long) time for the process to happen. A black hole can thus quantum-tunnel into a white hole. For this to happen, quantum gravity should affect the metric also in a small region outside the horizon: we show that contrary to what is commonly assumed, this is not forbidden by causality or by the semiclassical approximation, because quantum effects can pile up over a long time. This scenario alters radically the discussion on the black hole information puzzle.

173 citations

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TL;DR: In this article, the authors classify the possible alternatives to classical black holes and provide a minimal set of phenomenological parameters that describe their characteristic features, and perform an extensive analysis of different observational channels and obtain the most accurate characterization of the viable constraints that can be placed using current data.

Abstract: While singularities are inevitable in the classical theory of general relativity, it is commonly believed that they will not be present when quantum gravity effects are taken into account in a consistent framework. In particular, the structure of black holes should be modified in frameworks beyond general relativity that aim at regularizing singularities. Being agnostic on the nature of such theory, in this paper we classify the possible alternatives to classical black holes and provide a minimal set of phenomenological parameters that describe their characteristic features. The introduction of these parameters allows us to study, in a largely model-independent manner and taking into account all the relevant physics, the phenomenology associated with these quantum-modified black holes. We perform an extensive analysis of different observational channels and obtain the most accurate characterization of the viable constraints that can be placed using current data. Aside from facilitating a critical revision of previous work, this analysis also allows us to highlight how different channels are capable of probing certain features but are oblivious to others, and pinpoint the theoretical aspects that should be addressed in order to strengthen these tests.

171 citations

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TL;DR: In this paper, the authors point out that established physics includes objects with precisely the required properties for remnants: white holes with small masses but large finite interiors, and nonperturbative quantum gravity indicates that a black hole tunnels precisely into such a white hole, at the end of its evaporation.

Abstract: Quantum tunneling of a black hole into a white hole provides a model for the full life cycle of a black hole. The white hole acts as a long-lived remnant, providing a possible resolution to the information paradox. The remnant solution of the paradox has long been viewed with suspicion, mostly because remnants seemed to be such exotic objects. We point out that (i) established physics includes objects with precisely the required properties for remnants: white holes with small masses but large finite interiors; (ii) non-perturbative quantum gravity indicates that a black hole tunnels precisely into such a white hole, at the end of its evaporation. We address the objections to the existence of white-hole remnants, discuss their stability, and show how the notions of entropy relevant in this context allow them to evade several no-go arguments. A black hole’s formation, evaporation, tunneling to a white hole, and final slow decay, form a unitary process that does not violate any known physics.

143 citations

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TL;DR: In this paper, the amplitude of a gravitationally collapsed object bouncing out from its horizon via a tunnelling process that violates the classical equations in a finite region is computed in a background-free formulation of quantum gravity.

Abstract: A gravitationally collapsed object can bounce out from its horizon via a tunnelling process that violates the classical equations in a finite region. Since tunnelling is a nonperturbative phenomenon, it cannot be described in terms of quantum fluctuations around a classical solution, and a background-free formulation of quantum gravity is needed to analyze it. Here, we use loop quantum gravity to compute the amplitude for this process, in a first approximation. The amplitude determines the tunnelling time as a function of the mass. This is the key information to evaluate the relevance of this process for the interpretation of fast radio bursts or high-energy cosmic rays. The calculation offers a template and a concrete example of how a background-free quantum theory of gravity can be used to compute a realistic observable quantity.

127 citations

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TL;DR: In this paper, it is shown that the ignorance principle holds for the quantum-mechanical evaporation of black holes, where the black hole creates particles in pairs, with one particle always falling into the hole and the other possibly escaping to infinity.

Abstract: The principle of equivalence, which says that gravity couples to the energy-momentum tensor of matter, and the quantum-mechanical requirement that energy should be positive imply that gravity is always attractive. This leads to singularities in any reasonable theory of gravitation. A singularity is a place where the classical concepts of space and time break down as do all the known laws of physics because they are all formulated on a classical space-time background. In this paper it is claimed that this breakdown is not merely a result of our ignorance of the correct theory but that it represents a fundamental limitation to our ability to predict the future, a limitation that is analogous but additional to the limitation imposed by the normal quantum-mechanical uncertainty principle. The new limitation arises because general relativity allows the causal structure of space-time to be very different from that of Minkowski space. The interaction region can be bounded not only by an initial surface on which data are given and a final surface on which measurements are made but also a "hidden surface" about which the observer has only limited information such as the mass, angular momentum, and charge. Concerning this hidden surface one has a "principle of ignorance": The surface emits with equal probability all configurations of particles compatible with the observers limited knowledge. It is shown that the ignorance principle holds for the quantum-mechanical evaporation of black holes: The black hole creates particles in pairs, with one particle always falling into the hole and the other possibly escaping to infinity. Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state. This means there is no $S$ matrix for the process of black-hole formation and evaporation. Instead one has to introduce a new operator, called the superscattering operator, which maps density matrices describing the initial situation to density matrices describing the final situation.

2,226 citations

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TL;DR: In this article, the authors argue that the following three statements cannot all be true: (i) Hawking radiation is in a pure state, (ii) the information carried by the radiation is emitted from the region near the horizon, with low energy effective field theory valid beyond some microscopic distance from the horizon.

Abstract: We argue that the following three statements cannot all be true: (i) Hawking radiation is in a pure state, (ii) the information carried by the radiation is emitted from the region near the horizon, with low energy effective field theory valid beyond some microscopic distance from the horizon, and (iii) the infalling observer encounters nothing unusual at the horizon. Perhaps the most conservative resolution is that the infalling observer burns up at the horizon. Alternatives would seem to require novel dynamics that nevertheless cause notable violations of semiclassical physics at macroscopic distances from the horizon.

1,476 citations

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TL;DR: In this article, the authors argue that the following three statements cannot all be true: (i) Hawking radiation is in a pure state, (ii) the information carried by the radiation is emitted from the region near the horizon, with low energy effective field theory valid beyond some microscopic distance from the horizon.

Abstract: We argue that the following three statements cannot all be true: (i) Hawking radiation is in a pure state, (ii) the information carried by the radiation is emitted from the region near the horizon, with low energy effective field theory valid beyond some microscopic distance from the horizon, and (iii) the infalling observer encounters nothing unusual at the horizon. Perhaps the most conservative resolution is that the infalling observer burns up at the horizon. Alternatives would seem to require novel dynamics that nevertheless cause notable violations of semiclassical physics at macroscopic distances from the horizon.

1,201 citations

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TL;DR: If black hole formation evaporation can be described by an S matrix, information would be expected to come out in black hole radiation, but an estimate shows that it may come out initially so slowly, or else be so spread out, that it would never show up in an analysis perturbative in M/M.

Abstract: If black hole formation evaporation can be described by an S matrix, information would be expected to come out in black hole radiation. An estimate shows that it may come out initially so slowly, or else be so spread out, that it would never show up in an analysis perturbative in ${\mathit{M}}_{\mathrm{Planck}}$/M, or in 1/N for two-dimensional dilatonic black holes with a large number N of minimally coupled scalar fields.

1,061 citations

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TL;DR: In this paper, it is shown that small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole, and that one cannot explain away the information paradox by invoking AdS/CFT duality.

Abstract: The black hole information paradox is a very poorly understood problem. It is often believed that Hawking's argument is not precisely formulated, and a more careful accounting of naturally occurring quantum corrections will allow the radiation process to become unitary. We show that such is not the case, by proving that small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole. We formulate Hawking's argument as a 'theorem': assuming 'traditional' physics at the horizon and usual assumptions of locality we will be forced into mixed states or remnants. We also argue that one cannot explain away the problem by invoking AdS/CFT duality. We conclude with recent results on the quantum physics of black holes which show that the interior of black holes have a 'fuzzball' structure. This nontrivial structure of microstates resolves the information paradox and gives a qualitative picture of how classical intuition can break down in black hole physics.

1,024 citations