Nov 28, 2014 bekenstein hawking entropy from criticality. Hawking radiation and bekenstein hawking entropy are the two robust predictions of a yet unknown quantum theory of gravity. This is particularly true for the first and second laws. In 1972, bekenstein was the first to suggest that black holes should have a welldefined entropy. Albertathy 0398 thermal fields, entropy, and black holes v. I share some memories and offer a personal perspective on jacob bekenstein s legacy, focussing on black hole entropy and the bekenstein bound. By 1972, bekenstein had published three influential papers about the black hole stellar phenomenon, postulating the nohair theorem and presenting a theory on black hole thermodynamics. 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. Bekenstein s original argument, as suggestive as it may appear, thus fails. We suggested that the appropriate generalization of the second law for a region containing a black hole is that the blackhole entropy plus the. Thus, two black holes with the same area must have the same entropy, since otherwise one could violate the second law by penrose processes. In gravity, bekenstein hawking entropy is an entropy assigned to black hole, on the basis of laws of thermodynamics and observers outside black hole. Bekenstein has contributed to the foundation of black hole thermodynamics and. But a basic problem of these entropies is that the second law of thermodynamics is not guaranteed, in contrast to the bekenstein hawking entropy.
In the years to come, bekenstein continued his exploration of black holes, publishing papers on their entropy. The bekensteinhawking entropy of higherdimensional rotating. From shannon to bekenstein article pdf available in international journal of theoretical physics 5011 august 2010 with 110 reads how we measure reads. I want to show that the entanglement entropy between the two cfts corresponds approximately to the hawking bekenstein black hole entropy. The selection and focus is determined by my idiosyncracies, time limitations, and an e. Viewpoint a microscopic account of black hole entropy. We showthat it is natural to introduce the conceptof blackhole entropy as the measure. One then discusses the attempts to interpret the black hole entropy as. Jacob bekenstein pictured, the father of black hole thermodynamics, passed away in august. In gravity, bekensteinhawking entropy is an entropy assigned to black hole, on the basis of laws of thermodynamics and observers outside black hole. For higher n supergravities we just give an account of the general theory specializing the discussion to the n 8 case when one half of supersymmetry is preserved. Moreover, the entropy is found to be proportional to the bekensteinhawking entropy during the black hole evaporation.
Recently, exotic black holes whose masses and angular momenta are interchanged have been found in several different systems. I summarize a number of fascinating recent developments that grew out of bekenstein s pioneering contributions, from the ryutakayanagi proposal to the quantum null energy condition. Corrected bekensteinhawking entropy of warped ads 3. Lets do this for the 3d case also known as the btz black hole to keep it simple. Kaluzaklein state in bekensteinhawking entropy cycles. Black holes with mdrs and bekensteinhawking and perelman.
Microscopic derivation of the bekensteinhawking entropy. Thermodynamics of exotic black holes, negative temperature. In particular, n 2 supergravity in four dimensions is studied in detail. System upgrade on feb 12th during this period, ecommerce and registration of new users may not be available for up to 12 hours. A research student at princeton, bekenstein suggested a black hole s event horizon area was a measure of its entropy, or disorder.
A microscopic account of black hole entropy string theory provides a microscopic description of the entropy of certain theoretical black holes an important step toward understanding black hole thermodynamics. The constant of proportionality was determined by bekenstein and hawking in articles 5, 9, 10. The increase of the entropy of the black hole more than compensates for the decrease of the entropy carried by the object that was swallowed. Its rationalized area is given by at blackhole physics from the point of view of the theory of information. The black hole entropy is derived in terms of the bekensteinhawking law for a given horizon area of mass m and arbitrary real positive values. The bekenstein hawking 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. Using the case of black hole thermodynamics and bekenstein s celebrated argument for the entropy of black holes, i will argue that informationtheoretic notions are problematic in the present case. In the generalized uncertainty principle gup, there should be a minimal black hole whose size is comparable to the minimal length so that it cannot evaporate completely through the thermal radiation. Entropy, topology of twodimensional extreme black holes. Jacob bekenstein, towering theoretical physicist who studied.
In the 1970s, jacob bekenstein showed that black holes set a theoretical maximum on information storage, which applies to any quantum computer or, indeed, any physical system governed by quantum mechanics. Entropy and black holes bekenstein first had to define the entropy of a black hole to show that it is a thermal body. We discuss the most interesting approaches to derivation of the bekenstein hawking entropy formula from a. However, recently, based upon the study of topological properties, it. We study the warped ads3 rotating black hole and calculate the. Hawking added to the puzzle when he discovered that a black hole will. When common entropy goes down a black hole,the common entropy in the.
Well, it turns out that the amount of entropy a black hole has is proportional to its area, and he gave a formula which only the numerical constant was missing. Corrected bekensteinhawking entropy of warped ads 3 rotating. Bekenstein, statistical blackhole thermodynamics, phys. Starting from theorems proved by stephen hawking, jacob bekenstein conjectured that. Download it once and read it on your kindle device, pc, phones or tablets.
If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole. The analogy with the tendency of entropy to increase led me to propose in 1972 that a black hole has entropy proportional to. Fursaev 4 1 theoretical physics institute, department of physics, university of alberta, edmonton, canada t6g 2j1 2ciar cosmology and gravity program 3p. Use features like bookmarks, note taking and highlighting while reading of gravity, black holes, and information english books. It striking property is that it is proportional to the surface area of the balck holes horizon. Pando zayas1,2 i nthe 1970s, theorists determined that black holes have entropy 1, a remarkable. Hawking radiation with angular momentum and the entropy variation. To discuss this question on more clear terms, a nonboltzmannian entropic functional noted s. That, in turn, would mean that black holes must emit energy, though they previously werent thought to emit anything at all.
He had made major contributions to many areas of physics, including a proof of the nonexistence of scalar hair on a black hole, bounds on entropy and information, and a proposal for a modified theory of gravity that could provide an alternative to the presence. Bekenstein s generalized second law gsl of thermodynamics asserts that the sum of black hole entropy, s bh a c 3 4 h g here a is the black hole surface area, and the ordinary entropy of matter and radiation fields in the black hole exterior region never decreases. Our considerations also apply to higherdimensional black holes, although we have no derivation of the bekensteinhawking entropy formula in these cases. A keen teacher and mentor, he was also a key figure. Properties of classical black holes and both classical and quantum black hole thermodynamics are treated. Its rationalized area is given by at black hole physics from the point of view of the theory of information. We discuss the most interesting approaches to derivation of the.
This implies that the entropy of a black hole is a function only of its area. Of gravity, black holes, and information english books 2. 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. Extremal black holes in supergravity and the bekenstein. Bekenstein incorporated black hole entropy into a generalized second lawthat the sum of the entropy outside black holes plus the newly proposed entropy of black holes must never decreaseand carefully considered processes that might violate it.
Entanglement entropy of black holes 5 1 introduction one of the mysteries in modern physics is why black holes have an entropy. If we were to look at black holes, an observer would only be able to notice its mass, angular momentum, and electric charge. China abstract in this paper, we studythe bekensteinhawking entropy of higherdimensional rotating black holes from the euclidean pathintegral method proposed by gibbons and hawking. Quantum information and quantum black holes internet archive. We here reanalyze an intriguing gedanken experiment which was designed by bekenstein to challenge the gsl. The sum of the ordinary entropy of matter outside of a black hole plus a suitable. According to quantum mechanics, vacuum is no longer an empty state as in classical. It striking property is that it is proportional to the surface area of the balck hole s horizon properties interpretation in adscft correspondence. Jacob bekenstein, a physicist who prevailed in an argument with stephen hawking that revolutionized the study of black holes, and indeed the nature of.
Black hole bh thermodynamics was established by bekenstein and hawking, who made abstract theoretical arguments about the second law of thermodynamics. This conclusion is complemented by one sketched here. But the generalized second law introduced by bekenstein j d, 1974 bekenstein hawking entropy demands that the sum of ordinary entropy outside black holes and the total black hole entropy shall never decrease. Aug 22, 2015 jacob bekenstein, a physicist who prevailed in an argument with stephen hawking that revolutionized the study of black holes, and indeed the nature of spacetime itself, died on sunday in helsinki. The bekenstein bound or universal entropy bound is a limit on the entropy that can be contained in a physical system or object with given size and total energy bekenstein j d, 1981.
Of gravity, black holes, and information english books kindle edition by jacob d. He wrote that a black hole s entropy was proportional to the area of its the black hole s event horizon. The quantum corrected entropy is in precise numerical agreement with the logarithm of the number of microstates once quantum corrections are correctly taken into account. In ordinary statistical mechanics, the entropy s is a measure of the multiplicity of microstates that hide. Developments in black hole entropy jacob bekenstein. The bekensteinhawking entropy of higherdimensional. Jacob bekenstein, a black hole pioneer and hebrew university theoretical physicist, has died. In this talk i summarize some recent progress in string theory in understanding the entropy of a class of black holes including corrections to the bekensteinhawking formula.
The holographic principle has revealed that physical systems in 3d space, black holes included, are basically twodimensional as far as their information content is concerned. Black holes with mdrs and bekensteinhawking and perelman entropies for finslerlagrange. Recently, exotic black holes whose masses and angular momenta are interchanged have been found, and it is known that their entropies depend only on the inner horizon areas. Pdf empty black holes, firewalls, and the origin of. Since the schwarzschild \time coordinate t goes to in. The bekensteinhawking entropy of higherdimensional rotating black holes zheng ze ma. Thermodynamics of exotic black holes, negative temperature, and.
Bekenstein argued that no object can have more entropy than a black hole. In my opinion my derivation is just as rigorous as one based on quantum field theory. However, this no longer constitutes a problem, because hawking discovers a mechanism by which black holes can radiate. After a sequence of pecceiquinn transformations on the kaluzaklein state in cyclic cycles alternating between large and small extremal black hole ebh configurations, we obtain the corresponding amount of variation in the initial bekenstein hawking. Jul 30, 2015 in the generalized uncertainty principle gup, there should be a minimal black hole whose size is comparable to the minimal length so that it cannot evaporate completely through the thermal radiation. The bekenstein hawking entropy of a black hole, not considering quantum corrections, is onefourth of its horizon area 1,2.
Any theory which fails to reproduce these predictions is certainly incorrect. Jacob bekenstein, physicist who revolutionized theory of. Bekenstein did, aided by a great deal of mathematics, was to draw an analogy between the boundaries of black holes and the important physics concept known as entropy. Bekenstein also formulated the generalized second law of thermodynamics, black hole thermodynamics, for systems. The character of jacob bekenstein in a brief history of time. Lower limit on the entropy of black holes as inferred from. To do this, we have to look at the no hair theorem. Diagram of the positive mass ef spacetime, suppressing the angular coordinates, with constant r surfaces vertical and constant v surfaces at 45. Suppose black holes have an entropy s bh proportional to their area. Jan 14, 2018 i derive the bekenstein hawking formula for the entropy of a black hole. His insight, that black holes should have an entropy proportional to their area and a. The bekenstein entropy or black hole entropy is the amount of entropy.
A classical approach to set up the entropy of a black hole was given by gibbons. A kaluzaklein state configuration in black hole qubit correspondence bhqc is considered in cyclic cycles of its bekenstein hawking entropy. Jacob bekenstein, towering theoretical physicist who. Im currently doing a project on two sided adsschwarzschild black holes in the context of adscft. Vast amounts of interesting and important work on the subject are not mentioned.
Again, the black hole is not allowed to have a mass less than a scale of order planck mass, which suggested a black hole remnant. Department of physics, southeast university, nanjing, 210096, p. Black holes and entropy consider a kerr black hole of mass m, charge q, and angular momentum l. Black hole entropy is thermodynamic entropy future of humanity. This mechanism involves quantummechanical processes near the bh horizon. Historically, bekenstein estimated the entropy associated with a black hole in 1973, obtaining. Lebedev physics institute, leninskii prospect 53, moscow 117924, russia 4joint institute for nuclear research, laboratory of theoretical physics. Soon after that, this idea was put on a firm ground by hawking 128 who showed. First, the relation between black holes and limitations on information of other systems is developed. Logarithmic corrections to the bekensteinhawking entropy for. While several approaches lead to bekenstein hawking entropy, they all lead to different subleading corrections.
Picture of a black hole that forms from a collapsing shell of matter. In this article, we ask a question that is relevant for any approach. Thermodynamics, stability and hawkingpage transition of black. Chances are youve never heard of physicist jacob bekenstein, who devised a nifty formula for calculating a black hole s entropy. During the past three decades investigators have unveiled a number of deep connections between physical information and black holes whose consequences for ordinary systems go beyond what has been deduced purely from the axioms of information theory.
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