Integrability and associativity of the charge algebra are shown to require the inclusion. Black holes, entropy, and information ucsb physics. This identification of black hole area with entropy is made even stronger by the second law of thermodynamics and the hawking area theorem 4 which states that the area of black hole event horizons increases. Carlip that black hole entropy can be derived from a central charge of the virasoro algebra arising as a subalgebra in the surface deformations of general relativity in any dimension. Sep 05, 2019 but a mathematical black hole, the basis of black hole thermodynamics, is not the material from the star thats collapsed. Specifi cally this idea is used to provide a lower bound on the blackhole entropy to horizon area ratio using on ly a modicum of classical general relativity and rela tivastic quantum mechanics. Its rationalized area is given by at black hole physics from the point of view of the theory of information. The second law of thermodynamics says that entropy of a system either stays constant or increases it never decreases. The black hole information paradox and the black hole entropy are currently extensively researched. Although much progress has been made in in our understanding of. Black hole entropy i a black hole is a thermodynamic object endowed with energy, temperature, and entropy bekenstein, hawking, others 1970s i the energy is just the mass. Dear colleagues, in the four decades since its introduction into black hole physics, black hole entropy has proved a resilient and wideranging notion, with conceptual connections to a number of areas of the physical sciences, some far removed from black hole physics. Black hole entropy 2 the total energy of the black hole is mc2 so the number of such photons is n mc2 e gm2 hc 6 an estimate of the entropy is therefore s.
We showthat it is natural to introduce the conceptof blackhole entropy as the. Picture of a black hole that forms from a collapsing shell of matter. This is particularly true for the first and second laws. It seems that the apparently irreducible paradoxes force us to give up on at least one wellestablished principle. The fact that the blackhole entropy is also the maximal entropy that can be obtained by the bekenstein bound wherein the bekenstein bound becomes an equality was the main observation that led to. Since the schwarzschild \time coordinate t goes to in.
The entropy is basically a quantitative measure of what one knows about a black hole apart from its mass or spin. Blackhole thermodynamics including black holes in the scheme of thermodynamics has disclosed a deepseated connection between gravitation, heat and the quantum that may lead us to a synthesis of the corresponding branches of physics. This was not for a four dimensional black hole, but a rotating five dimensional black hole in kaluzaklein theory. In dimension d 4 an expansion of entanglement entropy in terms of size lof the subsystem outside the black hole is considered. Black hole information problem black hole basics there is a formal analogy between the properties of a black hole and thermodynamics. Virasoro r diffeomorphisms are presented which act nontrivially on the horizon of a generic kerr black hole with spin j. Primary among these are the black hole information paradox and issues related to the degrees of freedom responsible for the entropy of a black hole. Recently a precise calculation of the entropy of a neutral black hole in string theory was achieved emparan and gh, 2006.
This process is experimental and the keywords may be updated as the learning algorithm improves. Using the expression for the schwarzschild radius, the entropy of a black hole of eventhorizon area. The black hole information paradox, stephen hawkings. Some consider this to be the real black hole information paradox 72. It is shown that the entropy of a large nonrotating black hole is proportional to its horizon area. The fact that the black hole entropy is also the maximal entropy that can be obtained by the bekenstein bound wherein the bekenstein bound becomes an equality was the main observation that led to the holographic principle. A 2 24 rue lhomond, 75005 paris, france 3 school of natural sciences, institute for advanced study 4 department of physics, mcgill university 5 d.
All of the books ive read about the subject say that astronomicalscale black holes have very high entropy the exception being very small black holes created. However, a exactly the same thing could be said about black body radiation. A brief survey also is given of approaches to the calculation of black hole entropy. The constant of proportionality depends upon the immirzi parameter, which fixes the. Black hole entropy from poisson brackets demystification. Its rationalized area is given by at blackhole physics from the point of view of the theory of information.
Anomalies, chernsimons terms and black hole entropy pdf. Everyone knows that the entropy of a black hole is proportional to its area, and that there are only 3 parameters necessary to describe a black hole. Entropy free fulltext black hole entropy in scalar. Entropy is a measure of the energy unavailable to do work. The black hole entropy is proportional to the area of its event horizon. A major goal of research in quantum gravity is to provide an explanation forand direct derivation ofthe formula for the entropy of a black hole. Ellis, \the large scale structure of spacetime, cambridge university press. Pdf quantum geometry and black hole entropy semantic. First, you should note that there is a small error in your. We conclude with a discussion of some unresolved open issues.
There is a very deep result behind your question, which we are still figuring out the full meaning of. Black hole event horizon open string black hole solution black hole entropy these keywords were added by machine and not by the authors. Mock modular forms are beginning to appear more and more in many areas of physics. Since this is a short talk, we will mostly do this in the context of a. As mass is lost, the change in entropy will be ds 8 k c g mdm.
To discuss this question on more clear terms, a nonboltzmannian entropic functional noted s. Pdf black hole entropy quantization alejandro corichi. The quantum black hole degrees of freedom are shown to be described by a chernsimons field theory on the horizon. Lowermass black holes are expected to evaporate even faster. 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. For a solar mass black hole, the temperature is very low t 107 k so it is astrophysically negligible. E, s black hole lose entropy s gain black hole entropy.
Black hole entropy is a concept with geometric root but with many physical consequences. For entropy, it is indeed true that merging a black hole of mass m and entropy s with another equal mass black hole of mass m and entropy s will give you a new black hole with double the mass. Ever since the pioneer works of bekenstein and hawking, black hole entropy has been known to have a quantum origin. While this is not a resolution of the information paradox, we believe it provides. Entropy in thermodynamics and information theory wikipedia. To discuss this question on more clear terms, a nonboltzmannian entropic. Jhe anomalies, chernsimons terms and black hole pcf t cg tr 0 1 2 6. E 0 as the dropping point approaches the horizon, where. The blackhole entropy is proportional to the area of its event horizon.
Logarithmic corrections to black hole entropy, from the cardy. A small black hole has an entropy which is not exactly equal to a4. Logarithmic corrections to black hole entropy, from the cardy formula s carlip department of physics, university of california, davis, ca 95616, usa email. Information and blackhole entropy 2mr, q, where a lm, r, m. Pdf on jul 7, 2015, youssef ali albanay and others published black hole entropy find, read and cite all the research you need on. Revisiting the black hole entropy and the information paradox. Pdf on jul 7, 2015, youssef ali albanay and others published black hole entropy find, read and cite all the research you need on researchgate. Black hole thermodynamics including black holes in the scheme of thermodynamics has disclosed a deepseated connection between gravitation, heat and the quantum that may lead us to a synthesis of the corresponding branches of physics. The covariant phase space formalism provides a formula for the virasoro charges as surface integrals on the horizon. A black hole with the mass of a car would have a diameter of about 10. The thermodynamics of black hole apparent and event horizons in general relativity inspired the construction of a thermodynamics of spacetime by jacobson using local rindler horizons and assuming the entropyarea relation s a 4 g, where g is newtons constant we use units in which the speed of light c and the reduced planck constant. Diagram of the positive mass ef spacetime, suppressing the angular coordinates, with constant r surfaces vertical and constant v surfaces at 45. Ramanujans legacy used in signal processing, black hole.
One then discusses the attempts to interpret the black hole entropy as. We will now see that by asking for radial commutativity, the rt formula, and subregion duality to hold only in a subspace of the cft hilbert space, we can naturally realize all of them. Black hole thermodynamics introduction and motivation 5. Thus, it is said, hawking radiation is a quantum mechanical phenomenon. 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. A brief survey of work along these lines is provided in section 5. Stephen hawking raised profound issues concerning the loss of information in black hole evaporation and the consistency of quantum mechanics in a world with gravity. Integrability and associativity of the charge algebra are shown to require the inclusion of waldzoupas. Black hole entropy an introduction to thermal physics.
The second law again states that the entropy of a black hole system cannot decrease. It seems that the apparently irreducible paradoxes force us to give up on at least one well. Dec 22, 2019 thus, one can associate thermodynamic quantities like temperature and entropy to a black hole. An introduction to black holes, information and the string. One then discusses the attempts to interpret the black. Sep 10, 2014 the entropy of a black hole is then related to the surface area of its event horizon. Black holes and entropy consider a kerr black hole of mass m, charge q, and angular momentum l. The temperature of a black hole is inversely proportional to its mass. Let me begin by giving several reasons why we should not think that the. Here it is shown that the argumentation based on the reggeteitelboim approach is unsatisfactory. Mar 29, 2018 the idea for a black hole s entropy traces back to john wheeler, who was thinking about what happens to an object as it fall into a black hole from the point of view of an observer well outside. Integrability and associativity of the charge algebra are shown to require the.
Over the last decade the physics of black holes has been revolutionized by developments that grew out of jacob bekensteins realization that black holes have entropy. Generalized uncertainty principle and black hole entropy. This entropy was proposed as an unification of the wellknown s q of nonextensivestatistical mechanics and s. 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.
Generalized uncertainty principle and black hole entropy zhao rena,b. The defining expression for entropy in the theory of statistical mechanics established by ludwig boltzmann and j. Thus, one can associate thermodynamic quantities like temperature and entropy to a black hole. For a black hole with mass m, angular momentum j, and charge q these quantities are 4wr c gm a thus, after a few milliseconds the star has effectively gone out and what remains is an object which still exerts gravitational.
Many supersymmetric or nearsupersymmetric black holes in string theory admit a virl virr action of nontrivial or large diffeomorphisms 1,2. Recently, it has been shown that for certain extremal black holes the counting of microstates reproduces the black hole entropy including these subleading corrections. The idea for a black holes entropy traces back to john wheeler, who was thinking about what happens to an object as it fall into a black. The emphasis is on semiclassical gravity, so topics like string theory, dbranes, and superyang mills are discussed only very brie y. Chances are youve never heard of physicist jacob bekenstein, who devised a nifty formula for calculating a black holes entropy. Introductory lectures on black hole thermodynamics umd physics. But a mathematical black hole, the basis of black hole thermodynamics, is not the material from the star thats collapsed. Bekenstein to the physicist casually interested in gravitation, a black hole is a passive object.
A black hole has a singularity at a point inside of it where the curvature of space becomes infinite, i. Many recent attempts to calculate black hole entropy from. The derivation of hawking radiation confirmed the existence of black hole entropy and led to the formulation of black hole thermodynamics 2, 6. Some simple black hole thermodynamics stanford university.
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