DOCSLIB.ORG

Bekenstein Bound, Dark Matter, Dark Energy, Information Theory, Ordinary Matter

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Bekenstein Bound, Dark Matter, Dark Energy, Information Theory, Ordinary Matter American Journal of Computational and Applied Mathematics 2019, 9(2): 21-25 DOI: 10.5923/j.ajcam.20190902.01 On the Possible Ratio of Dark Energy, Ordinary Energy and Energy due to Information Boris Menin Mechanical & Refrigeration Consultation Expert, Beer-Sheba, Israel Abstract Information theory has penetrated into all spheres of human activity. Despite the huge number of articles on its application, the amount of scientific and technical research based on real results used in theory and in practice is relatively small. However, energy is central to life and society, both for stars and for galaxies. In particular, the energy density can be used for a consistent and unified explanation of the vast aggregate of various complex systems observed throughout Nature. This article proposes a discussion and calculations from simple and well-known studies that the energy density calculated using the information approach is a very useful metric for determining the amount of energy caused by information in the Universe. Keywords Bekenstein bound, Dark matter, Dark energy, Information theory, Ordinary matter and quantum mechanics. The results predicted future limits, 1. Introduction even far ahead, along which a road map was drawn up for adopting a set of solid conclusions regarding the limits of The definitions and methods of information theory, as computing. well as instruments and equipment developed on its basis, Some researchers suspect that eventually the axioms of have penetrated into all spheres of human activity: from quantum reconstruction will be related to information. To get biology and social sciences to astronomy and the theory of quantum mechanics out of the rules for what is allowed with gravity. The number of articles devoted to the application of quantum information, the authors [4] proposed three information theory to scientific and technological problems fundamental axioms. One of them was a direct consequence exceeds tens of thousands over the past twenty years. At the of the special theory of relativity: you cannot transfer same time, the number of scientific and technical studies information between two objects faster than the speed of devoted to practical applications and based on factual results light, making a measurement on one of the objects. The third is relatively small. axiom limits how securely you can exchange a little Information is universal. It easily passes between all information without being faked: this rule is a ban on what is physical structures. Its communication can be measured in called “unconditionally safe bit-commitment.” These axioms all of them by one common value, the bit. Information works seem to be related to the practice of managing quantum differently at different levels of complexity. However, all information. However, if we consider them fundamental, and this information has a real causal effect for complex systems suppose that the algebra of quantum theory has a property that transmit it. called noncommutation, it can be shown that these rules give Of particular note are the numerous efforts to apply the rise to superposition, entanglement, uncertainty, non-locality information concept in quantum mechanics and cosmology. and so on. Because information is a physical object [1, 2], the concept Another information-oriented reconstruction was of information can be used as a universal tool for solving proposed in 2009 [5]. To obtain quantum mechanics from the problems in these two areas. rules of what is allowed with quantum information, the In a very interesting study [3], there were several basic authors proposed three “reasonable axioms” related to restrictions on the processing of information from information ability: that the most elementary component of thermodynamics, information theory, the theory of relativity all systems can contain no more than one bit of information, that the state of a composite system consisting of subsystems * Corresponding author: is completely determined by measurements on its [email protected] (Boris Menin) subsystems and that you can convert any pure state to Published online at http://journal.sapub.org/ajcam Copyright © 2019 The Author(s). Published by Scientific & Academic Publishing another and back. These assumptions inevitably lead to the This work is licensed under the Creative Commons Attribution International probability of the classical and quantum style and to no other License (CC BY). http://creativecommons.org/licenses/by/4.0/ species. 22 Boris Menin: On the Possible Ratio of Dark Energy, Ordinary Energy and Energy due to Information Moreover, if you change axiom three to say that states are difference is surprisingly similar to the 120-order difference transformed continuously—gradually, and not in one big between the observed energy density and that calculated jump—you get only a quantum theory, not a classical one. using quantum mechanics. The discrepancy arises from the This means that the mathematical machinery of quantum fact that the positions of the stars can be explained with the mechanics has nothing to do with how the world really exists; help of quantum mechanics [12]. It seems reasonable to rather, it is just an appropriate structure that allows us to assume that the discrepancy between these numbers may be develop expectations and beliefs regarding the results of our due to the assumption that the classification of classical interventions. In fact, quantum probabilities do not tell us information can be considered physically significant. There that we will measure, but only what we should reasonably is a hint that information provides a ghostly foundation on expect to measure. which the laws of physics are based. This is an idea that has Some researchers suspected that eventually the axioms of gained strength among other physicists. quantum reconstruction will be related to information. The During the last two decades, many experiments have information must be localized in space and time so that the confirmed the picture: normal atoms make up only about 5 systems can encode information about each other and that percent of the total energy budget in the Universe. There is each process must be reversible so that the information is another 25 percent that is in the form of “dark matter.” Dark saved [6]. The author showed that the system governed by matter still senses gravity, but we do not observe it directly; it these rules shows all familiar quantum behaviors, such as acts as a glue that allows you to create structures such as superposition and entanglement. galaxies and clusters of galaxies. And then the rest–70 Two fundamental principles of information theory were percent–is dark energy, which should be responsible for the used to assert that dark energy, which causes an accelerating cosmic acceleration. expansion of the Universe, can be easily explained in terms What is the nature of the “dark matter” of this mysterious of the energy of holographic information [7]. The first is the material, which has a gravitational effect, but does not emit “Holographic Principle,” which states that “the full set of or absorb light? Astronomers do not know. Dark energy degrees of freedom for all particles inhabiting a certain constitutes a significant part of the entire contents of the region in space and time can be presented as if they were all Universe, but this was not always known. Attempts to find a located on the border of this space–time,” ‘t Hooft [8]. The way to measure or calculate the value of the vacuum energy second is the Landauer principle, which states that any density completely failed or gave results inconsistent with erasure of information occurring in the system will observations or other proven theoretical results. Some of necessarily lead to the system dissipating a certain minimum these results are theoretically implausible due to some amount of heat to its erased bit in its environment. This unrealistic assumptions on which the calculation model is amount of heat depends solely on the temperature in based. And some theoretical results are in conflict with accordance with the second law of thermodynamics [1]. The observations, and the conflict itself is caused by some authors argued that the combination of the holographic dubious hypotheses on which the theory is based. principle with the Landauer principle explains the constant Recent observations state that there is a certain amount of density of dark energy, explains the time of appearance of unknown dark energy in our universe, so the current dark energy as a significant force in recent space history, and expansion of our universe is accelerating. It is believed that also eliminates the need for a true cosmological constant. the pressure of dark energy is negative, and the density of The Gedankenexperiment (German: “thought dark energy is almost constant throughout the expansion of experiment”) has revealed a further connection between the universe. In [13], the authors showed that the law of information and the universe’s acceleration [9]. This thought conservation of energy in our Universe should be changed experiment considered the algorithmic information because, due to the expansion of the universe, more vacuum describing the baryons in the whole universe, but also applies energy is obtained. As a result, the pressure of dark energy to any large co-moving volume. It was easily shown that the will be zero if the total energy of our Universe increases. observed increasing star formation would have resulted in a This pressureless dark energy model is largely consistent decrease in the number of algorithmic information bits if the with current observations. expansion had not started to accelerate. To ensure the second This article continues attempts to apply information law is satisfied with no decrease in algorithmic information theory to solving some problems of cosmology. Using bit number, an approximate extra doubling of universe well-known and consistent formulas in the scientific volume is found to be required, as is indeed observed to have community, we will see that the information paradigm resulted directly from the recent period of acceleration [10].
Load more

Recommended publications
  • Upper Limit on the Thermodynamic Information Content of an Action Potential
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 4 February 2020 Upper limit on the thermodynamic information content of an action potential Sterling Street∗ Department of Cellular Biology, Franklin College of Arts and Sciences, University of Georgia, Athens, GA, USA February 2, 2020 Abstract In computational neuroscience, spiking neurons are often analyzed as computing devices that register bits of information, with each ac- tion potential carrying at most one bit of Shannon entropy. Here, I question this interpretation by using Landauer's principle to estimate an upper limit for the quantity of thermodynamic information that can be dissipated by a single action potential in a typical mammalian neuron. I show that an action potential in a typical mammalian cor- tical pyramidal cell can carry up to approximately 3.4 · 1011 natural units of thermodynamic information, or about 4.9 · 1011 bits of Shan- non entropy. This result suggests that an action potential can process much more information than a single bit of Shannon entropy. 1 Introduction \The fundamental constraint on brain design emerges from a law of physics. This law governs the costs of capturing, sending, and storing information. This law, embodied in a family of equa- tions developed by Claude Shannon, applies equally to a telephone line and a neural cable, equally to a silicon circuit and a neural circuit." { Peter Sterling and Simon Laughlin [1] ∗[email protected]. Keywords: information, entropy, energy, thermodynamics, Landauer's principle, action potential 1 © 2020 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 4 February 2020 Many hypotheses and theories analyze spiking neurons as binary electro- chemical switches [1-3].
    [Show full text]
  • Edward Witten (Slides)
    Introduction to Black Hole Thermodynamics Edward Witten, IAS Madan Lal Mehta Lecture, April 19, 2021 In the first half of this talk, I will explain some key points of black hole thermodynamics as it was developed in the 1970's. In the second half, I will explain some more contemporary results, though I will not be able to bring the story really up to date. I cannot explain all the high points in either half of the talk, unfortunately, as time will not allow. Black hole thermodynamics started with the work of Jacob Bekenstein (1972) who, inspired by questions from his advisor John Wheeler, asked what the Second Law of Thermodynamics means in the presence of a black hole. The Second Law says that, for an ordinary system, the \entropy" can only increase. However, if we toss a cup of tea into a black hole, the entropy seems to disappear. Bekenstein wanted to \generalize" the concept of entropy so that the Second Law would hold even in the presence of a black hole. For this, he wanted to assign an entropy to the black hole. What property of a black hole can only increase? It is not true that the black hole mass always increases. A rotating black hole, for instance, can lose mass as its rotation slows down. But there is a quantity that always increases: Stephen Hawking had just proved the \area theorem," which says that the area of the horizon of a black hole can only increase. So it was fairly natural for Bekenstein to propose that the entropy of a black hole should be a multiple of the horizon area.
    [Show full text]
  • Unitarity Entropy Bound: Solitons and Instantons
    Unitarity Entropy Bound: Solitons and Instantons Gia Dvali Arnold Sommerfeld Center, Ludwig-Maximilians-Universit¨at, Theresienstraße 37, 80333 M¨unchen, Germany, Max-Planck-Institut f¨ur Physik, F¨ohringer Ring 6, 80805 M¨unchen, Germany and Center for Cosmology and Particle Physics, Department of Physics, New York University, 726 Broadway, New York, NY 10003, USA (Dated: July 18, 2019) We show that non-perturbative entities such as solitons and instantons saturate bounds on entropy when the theory saturates unitarity. Simultaneously, the entropy becomes equal to the area of the soliton/instanton. This is strikingly similar to black hole entropy despite absence of gravity. We explain why this similarity is not an accident. We present a formulation that allows to apply the entropy bound to instantons. The new formulation also eliminates apparent violations of the Bekenstein entropy bound by some otherwise-consistent unitary systems. We observe that in QCD, an isolated instanton of fixed size and position violates the entropy bound for strong ’t Hooft coupling. At critical ’t Hooft coupling the instanton entropy is equal to its area. I. UNITARITY AND ENTROPY The explanation given in [4] to the above phenomenon is that the key role both in saturation of the entropy The Bekenstein entropy bound [1] (see also, [2]) bound as well as in its area-form is played by an inter- particle coupling constant α that controls perturbative Smax = MR, (1) unitarity of the theory. The idea is that the objects that puts an upper limit on the amount of information stored share the property (3) are maximally packed in the sense in a system of energy M and size R.
    [Show full text]
  • The Bekenstein Bound and Non-Perturbative Quantum Gravity
    enstein b ound and View metadata, citation and similar papers at core.ac.uk The Bek brought to you by CORE provided by CERN Document Server non-p erturbative quantum gravity Kirill V.Krasnov Bogolyubov Institute for Theoretical Physics, Kiev 143, Ukraine (March 19, 1996) We study quantum gravitational degrees of freedom of an arbitrarily chosen spatial region in the framework of lo op quantum gravity . The main question concerned is if the dimension of the Hilb ert space of states corresp onding to the same b oundary area satis es the Bekenstein b ound. We show that the dimension of such space formed by all kinematical quantum states, i.e. with the Hamiltonian constraint b eing not imp osed, is in nite. We make an assumption ab out the Hamiltonian's action, which is equivalent to the holographic hyp othesis, an which lead us to physical states (solutions of the Hamiltonian constraint) sp eci ed by data on the b oundary. The physical states which corresp ond to the same b oundary area A form a nite dimensional Hilb ert space and we show that its dimension 2 , where lies in the interval 0:55 < < 1:01. We discuss in general the is equial to exp A=l p arising notion of statistical mechanical entropy.For our particular case, when the only parameter sp ecifying the system's macrostate is the b oundary area, this entropy is given by S (A)= A.We discuss the p ossible implications of the result obtained for the black hole entropy. Among the results of the lo op approach to non-p erturbative quantum gravity the are several which, if taken seriously, tell us that the picture of geometry on scales small comparatively with our usual scales (on Planckian scales) lo oks quite di erently from the habitual picture of Riemannian geometry, and that the usual classical picture arises only on a coarse-graining.
    [Show full text]
  • The Question of an Upper Bound on Entropy
    Bekenstein has recently proposed that there exists a universal IC/82/119 •upper 'bound for the entropy of a system of energy E and maximum length INTERHAL REPORT scale R, (Limited distribution) (1) International Atomic Energy Agency and {.in the natural units c = * = k = l) with the maximum entropy being achieved Nations Educational Scientific and Cultural Organisation by a black hole. His original argument vas based on a contradiction with the INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS second lav of black hole thermodynamics if the bound did not apply. Unruh and Wald have argued that no such contradiction arises if the argument is considered in full detail. Thome has derived an internal contradiction within Bekenstein's argument by considering a non-cubic rectangular box being lowered into a black hole, and showing that the smaller, rather than the larger, length scale is required by Bekenstein's argument in that case. Since the smaller length scale could not apply in any case (it is violated THE QUESTION OF AS UPPER BOUND ON ENTROPX • by observation) he argues that Bekenstein's bound is not valid. We contend that the essence of Bekenstein's argument is not limited Asghar Qadir •• by black hole considerations. It is merely a counting of the maximum number International Centre for Theoretical physics, Trieste, Italy. of states in a finite system having a finite energy. Let the volume of the system be V and the energy E. Then the phase space volume is certainly bounded above by E^f since the momentum is bounded above by energy. For definiteness consider a cubic box of length L.
    [Show full text]
  • The Holographic Principle for General Backgrounds 2
    SU-ITP-99-48 hep-th/9911002 The Holographic Principle for General Backgrounds Raphael Bousso Department of Physics, Stanford University, Stanford, California 94305-4060 [email protected] Abstract. We aim to establish the holographic principle as a universal law, rather than a property only of static systems and special space-times. Our covariant formalism yields an upper bound on entropy which applies to both open and closed surfaces, independently of shape or location. It reduces to the Bekenstein bound whenever the latter is expected to hold, but complements it with novel bounds when gravity dominates. In particular, it remains valid in closed FRW cosmologies and in the interior of black holes. We give an explicit construction for obtaining holographic screens in arbitrary space-times (which need not have a boundary). This may aid the search for non-perturbative definitions of quantum gravity in space-times other than AdS. Based on a talk given at Strings ’99 (Postdam, Germany, July 1999). More details, references, and examples can be found in Refs. [1, 2]. 1. Entropy Bounds, Holographic Principle, and Quantum Gravity How many degrees of freedom are there in nature, at the most fundamental level? In arXiv:hep-th/9911002v1 2 Nov 1999 other words, how much information is required to specify a physical system completely? The world is usually described in terms of quantum fields living on some curved background. A Planck scale cutoff divides space into a grid of Planck cubes, each containing a few degrees of freedom. Applied to a spatially bounded system of volume V , this reasoning would seem to imply that the number of degrees of freedom, Ndof ,‡ is of the order of the volume, in Planck units: Ndof (V ) ∼ V.
    [Show full text]
  • Bekenstein Bound from the Pauli Principle∗
    Bekenstein bound from the Pauli principle∗ G. Acquaviva,1, y A. Iorio,1, z and L. Smaldone1, x 1Faculty of Mathematics and Physics, Charles University, V Holeˇsoviˇck´ach2, 18000 Praha 8, Czech Republic. Assuming that the degrees of freedom of a black hole are finite in number and of fermionic nature, we naturally obtain, within a second-quantized toy model of the evaporation, that the Bekenstein bound is a consequence of the Pauli exclusion principle for these fundamental degrees of freedom. We show that entanglement, Bekenstein and thermodynamic entropies of the black hole all stem from the same approach, based on the entropy operator whose structure is the one typical of Takahashi and Umezawa's Thermofield Dynamics. We then evaluate the von Neumann black hole{environment entropy and noticeably obtain a Page-like evolution. We finally show that this is a consequence of a duality between our model and a quantum dissipative-like fermionic system. I. INTRODUCTION identification with the standard formulae (see [7], where the bound is rigorously defined in quantum field theory This paper moves from the results of previous research (QFT) and, e.g., the review [8]) one needs to associate ge- [1], but reversing the point of view. There, Bekenstein's ometrical concepts to the Xons. For instance, one could argument that a black hole (BH) reaches the maximal make each dof correspond to one elementary Planck cell. entropy at disposal of a physical system (i.e., that it sat- Nonetheless, in our picture we do not need the exact ex- urates the Bekenstein bound [2]), leads to two main pro- pression of the bound.
    [Show full text]
  • A Proof of the Bekenstein Bound for Any Strength of Gravity Through Holography Alessandro Pesci
    A proof of the Bekenstein bound for any strength of gravity through holography Alessandro Pesci To cite this version: Alessandro Pesci. A proof of the Bekenstein bound for any strength of gravity through hologra- phy. Classical and Quantum Gravity, IOP Publishing, 2010, 27 (16), pp.165006. 10.1088/0264- 9381/27/16/165006. hal-00616263 HAL Id: hal-00616263 https://hal.archives-ouvertes.fr/hal-00616263 Submitted on 21 Aug 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Confidential: not for distribution. Submitted to IOP Publishing for peer review 14 May 2010 AproofoftheBekensteinboundforanystrengthofgravitythroughholography Alessandro Pesci∗ INFN-Bologna, Via Irnerio 46, I-40126 Bologna, Italy The universal entropy bound of Bekenstein is considered, at any strength of the gravitational interaction. A proof of it is given, provided the considered general-relativistic spacetimes allow for ameaningfulandinequivocaldefinitionofthequantitieswhichpartecipatetothebound(suchas system’s energy and radius). This is done assuming as starting point that, for assigned statistical- mechanical local conditions, a lower-limiting scale l∗ to system’s size definitely exists, being it required by holography through its semiclassical formulation as given by the generalized covariant entropy bound. An attempt is made also to draw some possible general consequences of the l∗ assumption with regards to the proliferation of species problem and to the viscosity to entropy density ratio.
    [Show full text]
  • Bekenstein Bound of Information Number N and Its Relation to Cosmological Parameters in a Universe with and Without Cosmological Constant
    Wilfrid Laurier University Scholars Commons @ Laurier Physics and Computer Science Faculty Publications Physics and Computer Science 2013 Bekenstein Bound of Information Number N and its Relation to Cosmological Parameters in a Universe with and without Cosmological Constant Ioannis Haranas Wilfrid Laurier University, [email protected] Ioannis Gkigkitzis East Carolina University, [email protected] Follow this and additional works at: https://scholars.wlu.ca/phys_faculty Part of the Mathematics Commons, and the Physics Commons Recommended Citation Haranas, I., Gkigkitzis, I. Bekenstein Bound of Information Number N and its Relation to Cosmological Parameters in a Universe with and without Cosmological Constant. Modern Physics Letters A 28:19 (2013). DOI: 10.1142/S0217732313500776 This Article is brought to you for free and open access by the Physics and Computer Science at Scholars Commons @ Laurier. It has been accepted for inclusion in Physics and Computer Science Faculty Publications by an authorized administrator of Scholars Commons @ Laurier. For more information, please contact [email protected]. Bekestein Bound of Information Number N and its Relation to Cosmological Parameters in a Universe with and without Cosmological Constant 1 2 Ioannis Haranas Ioannis Gkigkitzis 1 Department of Physics and Astronomy, York University 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada E-mail:[email protected] 1 Departments of Mathematics, East Carolina University 124 Austin Building, East Fifth Street, Greenville NC 27858-4353, USA E-mail: [email protected] Abstract Bekenstein has obtained is an upper limit on the entropy S, and from that, an information number bound N is deduced. In other words, this is the information contained within a given finite region of space that includes a finite amount of energy.
    [Show full text]
  • Bound States and the Bekenstein Bound
    Lawrence Berkeley National Laboratory Lawrence Berkeley National Laboratory Title Bound states and the Bekenstein bound Permalink https://escholarship.org/uc/item/78h37096 Author Bousso, Raphael Publication Date 2009-10-06 eScholarship.org Powered by the California Digital Library University of California LBNL-53860 Bound states and the Bekenstein bound Raphael Bousso Center for Theoretical Physics, Department of Physics University of California, Berkeley, CA 94720-7300, U.S.A. and Lawrence Berkeley National Laboratory, Berkeley, CA 94720-8162, U.S.A. This work was supported in part by the Director, Office of Science, Office of High Energy Physics, of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098. DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor The Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or The Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or The Regents of the University of California.
    [Show full text]
  • Jacob Bekenstein, Towering Theoretical Physicist Who Studied Black Holes, Dies at 68
    The Washington Post August 28, 2015 Jacob Bekenstein, towering theoretical physicist who studied black holes, dies at 68 by Martin Weil Jacob Bekenstein, one of the world’s foremost theoretical physicists, who used the power of thought to explore the invisible objects that are ranked among the wonders of the universe — black holes — died Aug. 16 in Helsinki. He was 68. The New York Times reported that the cause of death was a heart attack, citing confirmation by the Hebrew University in Jerusalem. Dr. Bekenstein was a longtime professor at the university and was in Finland for a lecture. He was at home in many realms of physics that were beloved by science fiction writers and were located at the frontiers of his discipline. In addition to black holes, they included quantum mechanics and general relativity, which is a theory of gravity. Among fellow scientists he was known as a founder of the field of black hole thermodynamics. That area of endeavor is considered significant in the search for an overarching theory embracing gravitation and quantum mechanics. To physicists, his reputation rested to a great degree on contributions he made to describing the true and complex nature of black holes. At one time, it was believed that absolutely nothing escaped black holes, that they would take in everything, emit nothing and become ever increasingly massive. That belief was founded on Einstein’s general relativity. It cloaked them in mystery and gave them a hold on the popular imagination. But owing in great measure to Dr. Bekenstein’s work and to the application of quantum theory, that view has been substantially altered.
    [Show full text]
  • Black Holes in Loop Quantum Gravity Alejandro Perez
    Black Holes in Loop Quantum Gravity Alejandro Perez To cite this version: Alejandro Perez. Black Holes in Loop Quantum Gravity. Rept.Prog.Phys., 2017, 80 (12), pp.126901. 10.1088/1361-6633/aa7e14. hal-01645217 HAL Id: hal-01645217 https://hal.archives-ouvertes.fr/hal-01645217 Submitted on 17 Apr 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Black Holes in Loop Quantum Gravity Alejandro Perez1 1 Centre de Physique Th´eorique,Aix Marseille Universit, Universit de Toulon, CNRS, UMR 7332, 13288 Marseille, France. This is a review of the results on black hole physics in the framework of loop quantum gravity. The key feature underlying the results is the discreteness of geometric quantities at the Planck scale predicted by this approach to quantum gravity. Quantum discreteness follows directly from the canonical quantization prescription when applied to the action of general relativity that is suitable for the coupling of gravity with gauge fields and specially with fermions. Planckian discreteness and causal considerations provide the basic structure for the understanding of the thermal properties of black holes close to equilibrium. Discreteness also provides a fresh new look at more (at the mo- ment) speculative issues such as those concerning the fate of information in black hole evaporation.
    [Show full text]