Juan maldacena discusses the latest advances in solving. The emphasis is on semiclassical gravity, so topics like string theory, dbranes, and superyang mills are discussed only very brie y. Finally, cosmological horizons to which thermodynamic considerations also apply 4 are special cases of isolated horizons. Pdf black holes, gravitational radiation and the universe pp 149170 cite as. The immirzi parameter measures the size of the quantum of area in planck units. However, this attempt gives divergent entropy which is in contradiction.
As the study of the statistical mechanics of blackbody radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of. Modesto, black hole interior from loop quantum gravity, adv. The quantum geometry approach to a quantum theory of gravity is reasonably well established now. After an introduction that discusses the main conceptual issues we present some details about the classical and quantum geometry of isolated horizons and their quantum geometry and then use this scheme to give a natural definition of the entropy of black holes. Quantum geometry and entanglement entropy of a black hole. The number of microscopic states that are consistent with a black hole of a given horizon area a0 are counted and the statistical entropy, as a function of the area, is obtained for a0 up to 550. Indeed, in 1972, the israeli physicist jacob bekenstein figured out that the area of the spherical event horizon of a black hole corresponds to its entropy. Recently, nonperturbative techniques have led to a quantum theory of geometry in which. The number of microscopic states that is consistent with a black hole of a given horizon area a0 are counted and the statistical entropy, as a function of the area, is obtained for a0 up to 550lp12. Quantum geometry and black hole entropy arxiv vanity. In the 1970s stephen hawking, motivated by the analogy between the law of increasing area of black hole event horizons and the second law of thermodynamics, performed a semiclassical calculation showing that black holes are in equilibrium with thermal radiation outside them, and that black hole entropy that is, the entropy of the black hole. The bekensteinhawking entropy or black hole entropy is the amount of entropy that must be assigned to a black hole in order for it to comply with the laws of thermodynamics as they are interpreted by observers external to that black hole. The increasing entropy of a black hole that evaporates by emitting hawking radiation is at odds with the predictions of quantum mechanics. The quantum black hole degrees of freedom are shown to be described by a chernsimons field theory on the horizon.
Why black hole interiors grow forever quanta magazine. We then nd a map from focks space representations ofthe virasoro. Nonextensive statistical mechanics and black hole entropy. T and hawking xed the proportionality constants for tand s t bh 2. Quantum gravity theories are relevant for very high energies that occurred e. It is these degrees of freedom that account for the black hole entropy in our approach. Pdf quantum geometry and black hole entropy semantic. In particular, entropy of btz black holes in three dimensional gravity exhibits the same logarithmic correction. Black hole entropy, marginal stability and mirror symmetry. This is the number of different possible microscopic arrangements of all the. Quantum geometry of isolated horizons and black hole entropy. Recently a precise calculation of the entropy of a neutral black hole in string theory was achieved emparan and gh, 2006.
One then discusses the attempts to interpret the black hole entropy as. Thus, it is said, hawking radiation is a quantum mechanical phenomenon. Quantum black holes within the loop quantum gravity lqg framework are considered. By abhay ashtekar, j c baez, a corichi and k v krasnov. Black hole quantum gravity event horizon black hole entropy flux line. Classical and quantum gravity quantum geometry and microscopic black hole entropy to cite this article. Rather, quantum geometry serves as a bridge to another large classical spacetime. Quantum black holes and black hole statistical mechanics typeii string theory on k3, dbranes, fivedimensional d1d5 system and exact counting formula, stromingervafa black hole and leading entropy, 4d5d lift, exact counting formula for fourdimensional dyonic black holes, siegel modular forms, wallcrossing phenomenon, contour prescription. In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of blackhole event horizons. Black hole entropy from indistinguishable quantum geometric. Nonextensive statistical mechanics and black hole entropy from.
In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. We consider the superconformal quantum mechanics associated to bps black holes in type iib calabiyau compactifications. This summary will focus on structural issues from a mathematical physics perspective. An improved estimate of black hole entropy in the quantum. This shrinkage continues until the horizon reaches the planck size the characteristic scale of quantum gravity or earlier 4, 5, at which point a quantum transition quantum tunneling happens at the horizon, turning it into the horizon of a white hole fig. Pdf quantum geometry and black hole entropy alejandro. A proper counting of states for black holes in the quantum geometry approach shows that the dominant configuration for spins are distributions that include spins exceeding onehalf at the punctures. This was not for a four dimensional black hole, but a rotating five dimensional black hole in kaluzaklein theory.
Quantum geometry and microscopic black hole entropy article pdf available in classical and quantum gravity 241 november 2006 with 56 reads how we measure reads. Black hole entropy and dynamics of quantum fluctuations. Nonminimal couplings, quantum geometry and blackhole. We argued that the actual value of the information retention time may be entropy lost by evaporating black hole entropy of emitted radiation halfway point information revealed. The purpose of this contribution is is to discuss black hole entropy in the loop quantum gravity.
The selection and focus is determined by my idiosyncracies, time limitations, and an e. Quantum geometry and microscopic black hole entropy arxiv. The sum of the ordinary entropy of matter outside of a black hole plus a suitable multiple of the area of a black hole never decreases. Viewing the black hole from outside, this suggests that that general relativity is giving us a thermodynamic approximate description of the system if we stay outside. This formalism suggests that torsion acts within a.
This papers shows how the entropy of a black hole is computed approximately by egravity theory. The gauge theory gives a precise description of the black hole and its surrounding geometry. Embolic aspects of black hole entropy international. The nal third of the course is on adscft, including correlation functions, black hole thermodynamics, and entanglement entropy. Quantum geometry and microscopic black hole entropy core. Related content the thermodynamic limit and black hole entropy in the area ensemble j fernando barbero g and eduardo j s villasenor.
The results are consistent with an asymptotic linear relation and a logarithmic correction with a coefficient. The issue was raised in works by krasnov 4 and rovelli 5. It is described in terms of a perfectly ordinary quantum mechanical system. The consensus about the solution of the information paradox is not yet reached, and it is not yet clear what can we learn about quantum gravity from these and the related research. Blackhole entropy from quantum geometry iopscience. Quantum geometry the modern loop quantum gravity using graphs and spinnetworks instead of the loops provides microscopic degrees of freedom that account for the blackhole entropy. It also gives a completely quantum mechanical description of. Rovelli, quantumgravity effects outside the horizon spark black to white hole tunneling, phys. In loop quantum gravity the quantum geometry of a black hole horizon consists of discrete nonperturbative quantum geometric excitations or punctures labeled by spins, which are responsible for the quantum area of the horizon. Quantum geometry and microscopic black hole entropy. The immirzi parameter also known as the barberoimmirzi parameter is a numerical coefficient appearing in loop quantum gravity lqg, a nonperturbative theory of quantum gravity. The quantum geometry of a crosssection of a black hole horizon in lqg is described by a topological twosphere with defects, usually called punctures, carrying spin 5 quantum numbers endowed by the edges of the spin network that represent the bulk quantum geometry. It is shown that the entropy of a large nonrotating black hole is proportional to its horizon area.
Revisiting the black hole entropy and the information paradox. Pdf black hole entropy from an su2invariant formulation of. This notion of bh requires a complete knowledge of a spacetime geometry. Properties of classical black holes and both classical and quantum black hole thermodynamics are treated. It seems that the apparently irreducible paradoxes force us to give up on at least one wellestablished principle.
Black hole entropy, finite geometry and mermin squares. Quantum area of the black hole with spin quantum numbers j 1. Quantum geometry the modern loop quantum gravity using graphs and spinnetworks instead of the loops provides microscopic degrees of freedom that account for the black hole entropy. Quantum mechanics suggests that there should be an exact description where entropy does not increase. For a black hole, it is the size of the region behind the horizon.
Pdf quantum geometry and black hole entropy semantic scholar. Black holes in loop quantum gravity archive ouverte hal. These theories also make statements for the entropy of a black hole. Dec 06, 2018 in that case, all the known properties of a black hole should trace to properties of this quantum system. For an ordinary quantum system, he said, this is the complexity of the state. This is particularly true for the first and second laws.
Using the earlier developed classical hamiltonian framework as the point of departure, we carry out a nonperturbative quantization of the sector of general. A potential lesson, according to douglas stanford, a black hole specialist at the institute for advanced study in princeton, new jersey, is that black holes have a type of internal clock that keeps time for a very long time. Black holes, entropy, and information ucsb physics. Thanks to the peculiar distorted relativistic geometry, the white hole. This quantum mechanics describes the dynamics of dbranes in the nearhorizon attractor geometry of the black hole. As a result, its value is currently fixed by matching the semiclassical black hole entropy, as calculated by stephen hawking, and the. If these punctures are compared to a gas of particles, then the spins associated with the punctures can be viewed as single puncture area levels analogous to single. It is then natural to ask if one can analyze the quantum geometry of isolated horizons in detail and account for entropy from statistical mechanical considerations. However, a exactly the same thing could be said about black body radiation. Black hole entropy includes and may be 100% vacuum entanglement it seems natural that gravity would cut off the entanglement of pairs separated by less than the planck length, since they would be engulfed in a virtual black hole. A black hole sector of nonperturbative canonical quantum gravity is introduced. It is pointed out that the black hole radiation consistent with hawking spectrum can be realized as an effect of quantum geometry using a dynamical formalism for diffeomorphism invariance which envisages a discretized unit of time in the planck scale. The final quantum isolated horizon framework was introduced by ashtekar et al 8. Hayden and i 2007 reexamined the black hole information retention time using tools from quantum shannon theory and the theory of approximate unitary tdesigns.
In this way, the computation of black hole entropy from basic principles became an important test for. The results are consistent with an asymptotic linear relation and a logarithmic correction with a. We use the injectivity radius of the induced metric on. The constant of proportionality depends upon the immirzi parameter, which fixes the spectrum. Quantum geometry the modern loop quantum gravity using graphs and spinnetworks instead of the loops provides microscopic.
Quantum geometry provides microscopic degrees of freedom that account for the black hole entropy. The quantum black hole degrees of freedom are shown. Geometry map and black hole entropy once the functions land l are promoted to be operators acting on fock space, themetric 1becomes awellde ned operator, denoted asds2,onthat space. Vast amounts of interesting and important work on the subject are not mentioned. Complementary perspectives and further details can be found in articles on loop quantum gravity, canonical formalism, quantum cosmology, black hole thermo. Black hole evolution traced out with loop quantum gravity. This raises the value of the immirzi parameter and the black hole entropy.
Quantum geometry provides microscopic degrees of freedom that account for the blackhole entropy. In many cases, the black hole entropy can be found by counting the number of chiral primaries in this quantum mechanics. As the study of the statistical mechanics of black body radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of. We have studied here black hole entropy in the framework of quantum geometry. A major goal of research in quantum gravity is to provide an explanation for and direct derivation of the formula for the entropy. Pdf quantum geometry and microscopic black hole entropy. There is a thermal radiation with a black body spectrum emitted by black holes due to quantum e ects. The framework describes a black hole in equilibrium surrounded by a quite. Then the entropy can be estimated by the quantum statistics and the hawking temperature, like the usual photon entropy computation. Black holes and the information paradox in string theory. Research article black hole entropy from indistinguishable.
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