A kaluzaklein state configuration in black hole qubit correspondence bhqc is considered in cyclic cycles of its bekenstein hawking entropy. Pdf empty black holes, firewalls, and the origin of. The bekenstein hawking entropy of a black hole, not considering quantum corrections, is onefourth of its horizon area 1,2. I share some memories and offer a personal perspective on jacob bekenstein s legacy, focussing on black hole entropy and the bekenstein bound. In the years to come, bekenstein continued his exploration of black holes, publishing papers on their entropy. Bekensteins generalized second law of thermodynamics. Jan 14, 2018 i derive the bekenstein hawking formula for the entropy of a black hole. We discuss the most interesting approaches to derivation of the bekenstein hawking entropy formula from a. One then discusses the attempts to interpret the black hole entropy as. We study the warped ads3 rotating black hole and calculate the. Black hole entropy is thermodynamic entropy future of humanity. 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. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole.
Im currently doing a project on two sided adsschwarzschild black holes in the context of adscft. Jacob bekenstein pictured, the father of black hole thermodynamics, passed away in august. Thermodynamics of exotic black holes, negative temperature. Viewpoint a microscopic account of black hole entropy. Nov 28, 2014 bekenstein hawking entropy from criticality.
The sum of the ordinary entropy of matter outside of a black hole plus a suitable. The selection and focus is determined by my idiosyncracies, time limitations, and an e. The bekensteinhawking entropy of higherdimensional rotating. Since the schwarzschild \time coordinate t goes to in.
Black hole bh thermodynamics was established by bekenstein and hawking, who made abstract theoretical arguments about the second law of thermodynamics. Albertathy 0398 thermal fields, entropy, and black holes v. 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. Black holes with mdrs and bekensteinhawking and perelman. Jacob bekenstein, physicist who revolutionized theory of. Aug 12, 20 meanwhile the entropy \s \ has gone out of sight of observers outside the hole. Logarithmic corrections to the bekensteinhawking entropy for. In particular, n 2 supergravity in four dimensions is studied in detail. Lower limit on the entropy of black holes as inferred from. He wrote that a black hole s entropy was proportional to the area of its the black hole s event horizon. 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. 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. When common entropy goes down a black hole,the common entropy in the. Black hole physics seems to provide at least two ways in which the second law of thermodynamics may be transcended or violated.
Entanglement entropy of black holes 5 1 introduction one of the mysteries in modern physics is why black holes have an entropy. Kaluzaklein state in bekensteinhawking entropy cycles. The constant of proportionality was determined by bekenstein and hawking in articles 5, 9, 10. 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. It striking property is that it is proportional to the surface area of the balck hole s horizon properties interpretation in adscft correspondence.
To do this, we have to look at the no hair theorem. Jacob bekenstein, a black hole pioneer and hebrew university theoretical physicist, has died. Diagram of the positive mass ef spacetime, suppressing the angular coordinates, with constant r surfaces vertical and constant v surfaces at 45. 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. In gravity, bekenstein hawking entropy is an entropy assigned to black hole, on the basis of laws of thermodynamics and observers outside black hole. Picture of a black hole that forms from a collapsing shell of matter. We study the warped ads3 rotating black hole and calculate.
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. A research student at princeton, bekenstein suggested a black hole s event horizon area was a measure of its entropy, or disorder. Hawking radiation and bekenstein hawking entropy are the two robust predictions of a yet unknown quantum theory of gravity. If we were to look at black holes, an observer would only be able to notice its mass, angular momentum, and electric charge. But a basic problem of these entropies is that the second law of thermodynamics is not guaranteed, in contrast to the bekenstein hawking entropy. However, recently, based upon the study of topological properties, it.
China abstract in this paper, we studythe bekensteinhawking entropy of higherdimensional rotating black holes from the euclidean pathintegral method proposed by gibbons and hawking. 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. 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. According to quantum mechanics, vacuum is no longer an empty state as in classical. In gravity, bekensteinhawking entropy is an entropy assigned to black hole, on the basis of laws of thermodynamics and observers outside black hole. Its rationalized area is given by at blackhole physics from the point of view of the theory of information. Link between hawkingbekenstein black hole entropy and. Bekenstein has contributed to the foundation of black hole thermodynamics and. First, the relation between black holes and limitations on information of other systems is developed. 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.
Recently, exotic black holes whose masses and angular momenta are interchanged have been found in several different systems. Entropy, topology of twodimensional extreme black holes. Lebedev physics institute, leninskii prospect 53, moscow 117924, russia 4joint institute for nuclear research, laboratory of theoretical physics. Of gravity, black holes, and information english books 2. Jacob bekenstein, towering theoretical physicist who studied. System upgrade on feb 12th during this period, ecommerce and registration of new users may not be available for up to 12 hours. Entropy free fulltext corrections to bekensteinhawking. Historically, bekenstein estimated the entropy associated with a black hole in 1973, obtaining. 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. That, in turn, would mean that black holes must emit energy, though they previously werent thought to emit anything at all. Microscopic derivation of the bekensteinhawking entropy.
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. Jacob bekenstein, a physicist who prevailed in an argument with stephen hawking that revolutionized the study of black holes, and indeed the nature of. Any theory which fails to reproduce these predictions is certainly incorrect. Extremal black holes in supergravity and the bekenstein. Our considerations also apply to higherdimensional black holes, although we have no derivation of the bekensteinhawking entropy formula in these cases. I want to show that the entanglement entropy between the two cfts corresponds approximately to the hawking bekenstein black hole entropy. This entropy, known as the bekensteinhawking entropy, was first introduced by bekenstein 18,19, 20 as a rather useful analogy.
Moreover, the entropy is found to be proportional to the bekensteinhawking entropy during the black hole evaporation. This conclusion is complemented by one sketched here. However, this no longer constitutes a problem, because hawking discovers a mechanism by which black holes can radiate. 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.
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. Bekenstein s original argument, as suggestive as it may appear, thus fails. Entropy and black holes bekenstein first had to define the entropy of a black hole to show that it is a thermal body. 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.
We suggested that the appropriate generalization of the second law for a region containing a black hole is that the blackhole entropy plus the. 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. In this article, we ask a question that is relevant for any approach. We discuss the most interesting approaches to derivation of the. In my opinion my derivation is just as rigorous as one based on quantum field theory. While several approaches lead to bekenstein hawking entropy, they all lead to different subleading corrections. Black holes have entropy, which is proportional to their area. Soon after that, this idea was put on a firm ground by hawking 128 who showed. A classical approach to set up the entropy of a black hole was given by gibbons.
This implies that the entropy of a black hole is a function only of its area. In ordinary statistical mechanics, the entropy s is a measure of the multiplicity of microstates that hide. The bekensteinhawking entropy of higherdimensional rotating black holes zheng ze ma. A keen teacher and mentor, he was also a key figure. Pando zayas1,2 i nthe 1970s, theorists determined that black holes have entropy 1, a remarkable. In 1972, bekenstein was the first to suggest that black holes should have a welldefined entropy. So, the following formula has appeared s bh a4g a42 pl, 1 where s bh is the bekensteinhawking entropy and pl p. Thermodynamics of exotic black holes, negative temperature, and bekensteinhawking entropy. 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. Corrected bekensteinhawking entropy of warped ads 3 rotating. Its rationalized area is given by at black hole physics from the point of view of the theory of information. Suppose black holes have an entropy s bh proportional to their area. To discuss this question on more clear terms, a nonboltzmannian entropic functional noted s.
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. Quantum information and quantum black holes internet archive. Bekenstein argued that no object can have more entropy than a black hole. Use features like bookmarks, note taking and highlighting while reading of gravity, black holes, and information english books. 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. Jacob david bekenstein died of a heart attack on 16 august 2015 in helsinki, finland, where he was visiting to present a seminar. Thermodynamics, stability and hawkingpage transition of black. 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. This mechanism involves quantummechanical processes near the bh horizon. It striking property is that it is proportional to the surface area of the balck holes horizon. The character of jacob bekenstein in a brief history of time. Bekenstein also formulated the generalized second law of thermodynamics, black hole thermodynamics, for systems.
Black holes with mdrs and bekensteinhawking and perelman entropies for finslerlagrange. The analogy with the tendency of entropy to increase led me to propose in 1972 that a black hole has entropy proportional to. 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. Download it once and read it on your kindle device, pc, phones or tablets. 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. 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. Jacob bekenstein, towering theoretical physicist who. Department of physics, southeast university, nanjing, 210096, p. Properties of classical black holes and both classical and quantum black hole thermodynamics are treated. Bekenstein, statistical blackhole thermodynamics, phys. Fursaev 4 1 theoretical physics institute, department of physics, university of alberta, edmonton, canada t6g 2j1 2ciar cosmology and gravity program 3p. Hawking added to the puzzle when he discovered that a black hole will.
We showthat it is natural to introduce the conceptof blackhole entropy as the measure. Starting from theorems proved by stephen hawking, jacob bekenstein conjectured that. His insight, that black holes should have an entropy proportional to their area and a. Developments in black hole entropy jacob bekenstein. 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. This is particularly true for the first and second laws. From shannon to bekenstein article pdf available in international journal of theoretical physics 5011 august 2010 with 110 reads how we measure reads. Chances are youve never heard of physicist jacob bekenstein, who devised a nifty formula for calculating a black hole s entropy. The bekensteinhawking entropy of higherdimensional.
Hawking radiation with angular momentum and the entropy variation. The bekenstein entropy or black hole entropy is the amount of entropy. Vast amounts of interesting and important work on the subject are not mentioned. Thus, two black holes with the same area must have the same entropy, since otherwise one could violate the second law by penrose processes. We here reanalyze an intriguing gedanken experiment which was designed by bekenstein to challenge the gsl. 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. Black holes and entropy consider a kerr black hole of mass m, charge q, and angular momentum l. 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.
Thermodynamics of exotic black holes, negative temperature, and. 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. 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 holographic principle has revealed that physical systems in 3d space, black holes included, are basically twodimensional as far as their information content is concerned.