Conservative solutions to the black hole information problem

Nuclear Physics B - Proceedings Supplements, 1995

In these lectures, the author's point of view on the problem of Hawking Evaporation of Black Holes is explained in some detail. A possible resolution of the information loss paradox is proposed, which is fully in accord with the rules of quantum mechanics. Black hole formation and evaporation leaves over a remnant which looks pointlike to an external observer with low resolving power, but actually contains a new infinite asymptotic region of space. Information can be lost to this new region without violating the rules of quantum mechanics. However, the thermodynamic nature of black holes can only be understood by studying the results of measurements that probe extremely small (sub-Planck scale) distances and times near the horizon. Susskind's description of these measurements in terms of string theory may provide an understanding of the Bekenstein-Hawking (BH) entropy in terms of the states of stranded strings that cross the horizon. The extreme nonlocality of string theory when viewed at short time scales allows one to evade all causality arguments which pretend to prove that the information encoded in the BH entropy can only * Lectures given at the Spring School on Supersymmetry, Supergravity, and Superstrings, Trieste, March 1994. Supported in part by the Department of Energy under grant No. DE-FG05-90ER40559. be accessed by the external observer in times much longer than the black hole evaporation time. The present author believes however that the information lost in black hole evaporation is generically larger than the BH entropy, and that the remaining information is causually separated from the external world in the expanding horn of a black hole remnant or cornucopion. The possible observational signatures of such cornucopions are briefly discussed.

Int.J.Theor.Math.Phys. 2N2 (2012) 5-9, 2012

The discovery that black holes emit thermal type radiation changed radically our perception of their behavior sinve it means that some amount of information eventually returns to the universe outside the black hole. Then rises the question whether it is the whole of this information that goes back to the universe during the black hole evaporation or not. Numerous theories supporting either information preservation or extinction have been developed ever since. A new idea is proposed, based on a deep re-examination of what information is and what are its properties. We postulate that not all kinds of information are of equal importance to nature and, as a result, some of them should be preserved under any conditions, while the rest are allowed to be destroyed, so both preservation and destruction of information is what actually happens during the black hole formation/evaporation process.

AIP Conference Proceedings, 2009

The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the constraint and Hamiltonian operators. Matter-gravity entanglement is an inherent feature of physical states, whether or not there is a black hole. Matter fields alone are an open system with a non-unitary evolution. However, if there is a successful theory of quantum gravity, there is no information loss.

A coarse-grained description for the formation and evaporation of a black hole is given within the framework of a unitary theory of quantum gravity preserving locality, without dropping the information that manifests as macroscopic properties of the state at late times. The resulting picture depends strongly on the reference frame one chooses to describe the process. In one description based on a reference frame in which the reference point stays outside the black hole horizon for sufficiently long time, a late black hole state becomes a superposition of black holes in different locations and with different spins, even if the back hole is formed from collapsing matter that had a well-defined classical configuration with no angular momentum. The information about the initial state is partly encoded in relative coefficients---especially phases---of the terms representing macroscopically different geometries. In another description in which the reference point enters into the black hole horizon at late times, an S-matrix description in the asymptotically Minkowski spacetime is not applicable, but it sill allows for an "S-matrix" description in the full quantum gravitational Hilbert space including singularity states. Relations between different descriptions are given by unitary transformations acting on the full Hilbert space, and they in general involve superpositions of "distant" and "infalling" descriptions. Despite the intrinsically quantum mechanical nature of the black hole state, measurements performed by a classical physical observer are consistent with those implied by general relativity. In particular, the recently-considered firewall phenomenon can occur only for an exponentially fine-tuned (and intrinsically quantum mechanical) initial state, analogous to an entropy decreasing process in a system with large degrees of freedom.

2005

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 approach which makes use of some ingredients of earlier proposals. [Based on Talks given at ERE2004 "Beyond General Relativity", Miraflores de la Sierra, Madrid (Sept 2004), and at CERN (Oct 2004)].

arXiv (Cornell University), 2007

Using the Landauer's principle of information erasure, we show that the statement "the Schwarzschild black hole is a maximal entropy object" implies that its entropy is given by mass-squared. We also obtain the quantized black hole mass spectra and entropy by using the fact that the information is composed of bit or trit. The black hole entropy has a sub-leading contribution proportional to the logarithm of area in addition to the usual areal term without an artificial cutoff. Comparing the results with the analysis of Hod \cite{Hod}, we argue that the Schwarzschild black hole erases information in unit of trit. We also argue that the minimum of a black hole mass is $\sqrt{\log 3/(8\pi)}M_P$.

General Relativity and Gravitation, 2015

The two-point function 2. The Hadamard Ansatz 3. The non-Hadamard behavior B. Proof of well defined foliation C. Useful integrals to define ζ D. The SSC Formalism and the Sudden Collapse of the quantum state References I. INTRODUCTION The surprising discovery of black hole radiation by S. Hawking [3] in the 1970's, has had an enormous influence in our ideas concerning the interface of quantum theory and gravitation. For instance, it has changed our perception regarding the laws of black hole thermodynamics, which, before that discovery, could have been regarded as mere analogies to our current view that they represent simply the ordinary thermodynamical laws, as they apply to situations involving black holes (see for instance[51]). This, in turn, has led to the quest to understand, on statistical mechanical terms, and within different proposals for a theory of quantum gravity, the area of the black hole horizon as a measure of the black hole entropy. In fact, the most popular programs in this regard, String Theory and Loop Quantum Gravity, have important success in this front. Furthermore, the fact that as the black hole radiates it must lose mass leads to some tension between the picture that emerges from the gravitational side and the basic tenants of quantum theory. This tension was first pointed out by Hawking [4] and has even been described by many theorists as the "Black Hole Information Paradox" (BHIP). The root of the tension is that, according to the picture that emerges from the gravitational side, it seems that one can start with a pure initial quantum state characterizing the system at some initial stage, which then evolves into something that, at the quantum level, can only be characterized as a highly mixed quantum state, while, the standard quantum mechanical considerations would lead one to expect a fully unitary evolution. There is even some debate as to whether or not this issue should be considered as paradoxical.

General Relativity and Gravitation, 2010

The trans-Planckian and information loss problems are usually discussed in the literature as separate issues concerning the nature of Hawking radiation. Here we instead argue that they are intimately linked, and can be understood as "two sides of the same coin" once it is accepted that general relativity is an effective field theory.

Physical Review Letters, 2007

Can quantum-information theory shed light on black-hole evaporation? By entangling the in-fallen matter with an external system we show that the black-hole information paradox becomes more severe, even for cosmologically sized black holes. We rule out the possibility that the information about the infallen matter might hide in correlations between the Hawking radiation and the internal states of the black hole. As a consequence, either unitarity or Hawking's semiclassical predictions must break down. Any resolution of the black-hole information crisis must elucidate one of these possibilities.

arXiv (Cornell University), 2014

We propose a combination of two mechanisms that can resolve the black hole information paradox. The first process is that the black hole shrinks by a first order transition, since we assume the entropy is discontinuous. The black hole disappears. The second type of processes conserves unitarity. We assume that within the black hole micro-reversible quantum mechanical processes take place. These are ordinary particle processes, e.g. the decay of an electron and a positron into two photons.