In ordinary thermodynamics the third law may be stated in two ways: From formula (11) it is clear that the black hole temperature Information about registration may be found here. Many researchers now find themselves working away from their institutions and, thus, may have trouble accessing the Physical Review journals. The fact that the black hole entropy is also the maximal entropy that can be squeezed within a fixed volume was the main observation that led to the holographic principle. Both contributions were affirmed when Stephen Hawking (and, independently, Zeldovich and others) proposed the existence of Hawking radiationtwo years later. 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. \]. Jacob Bekenstein : biography 01 May 1947 – Jacob David Bekenstein (Hebrew: יעקב בקנשטיין) (born May 1, 1947) is an Israeli theoretical physicist who has contributed to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation. Jacob D. Bekenstein, Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel. Black hole entropy counts the number of states or excitations of a fundamental string. Of course, if the entropy in the usual (chemist's) form is required, the above should be multiplied by Boltzmann's constant \(k\ .\), For the spherically symmetric and stationary, or Schwarzschild, black hole (see Schwarzschild metric), the only parameter is the black hole's mass\(M\ ,\) the horizon's radius is \(r_h=2GM/c^2\ ,\) and its area is naturally given by \(4\pi r_h^2\ ,\) or : Physical Review D, 48, 3427 (1993) (, Witten, E.: Advances in Theoretical and Mathematical Physics, 2, 253 (1998) (, Zwiebach, B.: A first course in string theory, Cambridge University Press, Cambridge (2004), Teviet Creighton and Richard H. Price (2008), Hawking, S.W. A stationary black hole is parametrized by just a few numbers (Ruffini and Wheeler 1971): its mass, electric charge and angular momentum (and magnetic monopole charge, except its actual existence in nature has not been demonstrated yet). Sad news reached Jen-Luc Piquant this morning via Jonathan Oppenheim's Twitter feed: physicist Jacob Bekenstein, a professor at the Hebrew University of Jerusalem, passed away last night. One way to understand why is to recall the "area theorem" (Hawking 1971, Misner, Thorne and Wheeler 1973): the event horizon area of a black hole cannot decrease; it increases in most transformations of the black hole. Jacob David Bekenstein (Hebrew: יעקב בקנשטיין; May 1, 1947 – August 16, 2015) was a Mexico-born Israeli-American theoretical physicist who made fundamental contributions to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation. \Phi_{BH}\equiv Qr_h\Big(r_h^2+(J/Mc)^2\Big)^{-1}. \), \(\tag{10} Jacob Bekenstein, a physicist who prevailed in an argument with Stephen Hawking that revolutionized the study of black holes, and indeed the nature of … Through this difficult time APS and the Physical Review editorial office are fully equipped and actively working to support researchers by continuing to carry out all editorial and peer-review functions and publish research in the journals as well as minimizing disruption to journal access. ‎Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. After a brief review of the elements of the theory of information, we discuss black-hole physics from the point of view of information theory. Figure 1: The Bekenstein-Hawking entropy is the entropy ascribed to a black hole. Subscription Black hole entropy in string theory 5 4. Jacob David Bekenstein (Hebrew: יעקב בקנשטיין; May 1, 1947 – August 16, 2015) was an Israeli-American theoretical physicist who made fundamental contributions to the foundation of black hole thermodynamics and to other aspects of the connections between information and gravitation. We show that it is natural to introduce the concept of black-hole entropy as the measure of information about a black-hole interior which is inaccessible to an exterior observer. \], \[\tag{12} ‎Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. and Black Hole Entropy By |Jennifer Ouellette August 17, 2015 | The Bekenstein–Hawking entropy formula for a black hole. r=r_h\equiv GM/c^2+\sqrt{(GM/c^2)^2-(G^{1/2}Q/c^2)^2-(J/Mc)^2}. This page has been accessed 207,304 times. Developments in Black Hole Entropy. Varied theoretical arguments have been given in support of the GSL (Frolov and Page 1993, Bombelli et al. The validity of this version of the second law is supported by an argument from information theory as well as by several examples. In particular, certain string theories in five dimensional Anti-deSitter (AdS) spacetime are so mapped to conformal field theories on the corresponding spacetime's four-dimensional boundary which bears some resemblance to Minkowski spacetime (Maldacena et al. Jacob David Bekenstein was born in Mexico City on May 1, 1947. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. Dr. Bekenstein did his undergraduate work at Polytechnic Institute of Brooklyn. This has been taken to mean that there is a one-to-one correspondence between black hole and string states, where both entities have the same entropy (Susskind 1993). 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. This is quite in contrast with black hole entropy. We here re-analyze an intriguing gedanken experiment which was designed by Bekenstein to challenge the GSL. Thus a thermodynamic description of the collapse from that observer's viewpoint cannot be based on the entropy of that matter or radiation because these are unobservable. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. Bekenstein also formulated the generalized second law of thermodynamics, black hole thermodynamics , for systems including black holes. \Theta\equiv c^4(2GA)^{-1}(r_h-GM/c^2); We give a brief overview of black hole entropy, covering main developments since Bekenstein’s original proposal. : Communications Mathematical Physics, 43, 199 (1975), Hawking S.W. \[\tag{4} sufficiently slowly) reducing the string coupling constant (GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2=0. Bekenstein, Jacob D. There are a number of similarities between black-hole physics and thermodynamics. (GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2=0. This has been verified amply (Bekenstein 1975, Hawking 1976), and stands as testament to the predictive power of the GSL which was formulated two years before the Hawking radiation was put in evidence. How to express the black hole entropy in a concrete formula? Jacob David Bekenstein, né le 1 er mai 1947 à Mexico et mort le 16 août 2015 à Helsinki [1], [2], est un physicien israélo-mexicain. Loading ... Close Figure Viewer. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. and Black Hole Entropy By |Jennifer Ouellette August 17, 2015 | The Bekenstein–Hawking entropy formula for a black hole. Strings in string theory have a variety of excitations, so there is a multitude of string states. Downloaded 7 times History. Calculation (Bombelli et al. A=\int_0^\pi d\theta\int_0^{2\pi} d\varphi\sqrt{g_{\theta\theta}\, g_{\varphi\varphi}} = 4\pi(r_h^2+(J/Mc)^2). Black hole entropy is a concept with geometric root but with many physical consequences. Caption. Sadly, Jacob Bekenstein, the forefather of black hole thermodynamics affiliated with the Hebrew University in Jerusalem, died in Helsinki on Sunday night. This analogy suggests that black hole mass M might have a discrete spectrum. In 1972, Bekenstein was the first to suggest that black holes should have a well-defined entropy. A=16\pi(GM/c^2)^2 The honor recognized his groundbreaking work on black hole entropy and the pathways it opened to understanding of the cosmos. Thermodynamic entropy quantifies the said multiplicity. This has been verified by examples (Bekenstein 1973). This page was last modified on 25 April 2017, at 22:15. \], \(\tag{13} Agreement. This is particularly true for the first and second laws. A different approach making use of the specific properties of Kerr black holes and of concepts from information theory leads to the same conclusion, and suggests a definite value for the constant. the user has read and agrees to our Terms and ©2021 American Physical Society. : Gen. Rel. Is it meaningful or desirable to associate entropy with it ? The differential \(dA\) from equation (4), when multiplied by a suitable factor, takes the form We here re-analyze an intriguing gedanken experiment which was designed by Bekenstein to challenge the GSL. Use of the American Physical Society websites and journals implies that Jacob David Bekenstein hebr. Zwiebach 2004). Public domain, via Wikimedia Commons. Conditions and any applicable 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. Search for more papers by this author ... Jacob Bekenstein. He was hoping to disprove the contention of Jacob Bekenstein, then a graduate student at Princeton and now a professor at the Hebrew University in Jerusalem, that the area of a black hole’s boundary, the point of no return in space, was a measure of the entropy of a black hole. We appreciate your continued effort and commitment to helping advance science, and allowing us to publish the best physics journals in the world. Bekenstein showed that a fundamental limit on information density existed, the Bekenstein Bound and, like with a black hole's entropy, was … To address this, we have been improving access via several different mechanisms. When the system is one rotating with angular frequency \(\Omega\) and charged up to electric potential \(\Phi\), the changes in its angular momentum \(J\) and charge \(Q\) contribute the work The physical content of the concept of black-hole entropy derives from the following generalized version of the second law: When common entropy goes down a black hole, the common entropy in the black-hole exterior plus the black-hole entropy never decreases. Physical Review Physics Education Research, Log in with individual APS Journal Account », Log in with a username/password provided by your institution », Get access through a U.S. public or high school library ». It has been suggested that the sought for states are the states of the gravitational degrees of freedom residing on the black hole's horizon. Black Holes and Entropy* Jacob D. Bekensteing Joseph Henry Laboratories, Princeton University, Princeton, Neu Jersey OS540 and Center for Relativity Theory, The University of Texas at Austin, Austin, Texas 78712|: P,eceived 2 November 1972) There are a number of similarities between black-hole physics and thermodynamics. \ .\]. In 1972, Bekenstein was the first to suggest that black holes should have a well-defined entropy. This abstract approach has been championed by Wald (1993) as a road to black hole entropy in more general theories of gravity than general relativity. And we hope you, and your loved ones, are staying safe and healthy. S_{BH}={A\over 4 L_{P}^2}={c^3 A\over 4 G \hbar}, Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. T_{BH}=4 L_P^2 \Theta ={ \hbar c\over 2\pi} {\sqrt{(GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2}\over r_h^2+(J/Mc)^2} 1. Review of Bekenstein-Hawking Entropy 1 1.1 Metric 1 1.2 Black hole themodynamics 2 2. This article appears in the following collections: The editors of the Physical Review journals have curated a collection of landmark papers on General Relativity to celebrate its centennial. During the process of Hawking radiation the black hole's area decreases (basically because of the decrement of black hole mass), in violation of the area theorem. This increasing behavior is reminiscent of thermodynamic entropy of closed systems. it participates in the second law, many have wondered what the microstates that are counted by black hole entropy are. En 1973, Bekenstein fut le premier à suggérer que les trous noirs puissent avoir une entropie bien définie. \], \[\tag{3} For example, it is directly related to the hole's angular velocity in equation (9), and angular velocity of a thermodynamic system is an intensive parameter. Jacob Bekenstein andthe Development of Black Hole Thermodynamics Robert M. Wald∗ Enrico FermiInstitute andDepartmentof Physics, The University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA Abstract I give some personal reflections on Jacob Bekenstein’s pioneering work on associating an entropy It will be the first law if black hole entropy is required to be a function of \(A\) and of nothing else, so that \(dS_{BH}\propto dA\) (Gour and Mayo 2001). Rudiments of statistical mechanics 4 3. A black hole may be described as a blemish in spacetime, or a locale of very high curvature. He was awarded the Wolf Prize in … This discovery provided the calibration of the numerical factor in equation (1). Previous Figure Next Figure. Dr. Hawking’s celebrated breakthrough resulted partly from a fight. Metrics. To avoid violations, he found that he had to assume limitations on how close to the black hole’s horizon one could lower matter. Education Bekenstein received his undergraduate education in the Polytechnic University (now : Physical Review Letters, 93, 3902 (1993) (, Frolov, V. and Novikov, I.: Physical Review D, 48, 4545 (1993) (, Gour, G. and Mayo, A.M.: Physical Review D, 63, 064005 (2001) (, Hawking S.W. Including the black hole entropy in the entropy ledger gives a more useful law, the generalized second law of thermodynamics (GSL) (Bekenstein 1972, 1973, 1974): the sum of ordinary entropy \(S_o\) outside black holes and the total black hole entropy never decreases and typically increases as a consequence of generic transformations of the black hole. Bekenstein incorporated black hole entropy into a generalized second law—that the sum of the entropy outside black holes plus the newly proposed entropy of black holes must never decrease—and carefully considered processes that might violate it. The subscript BH either stands for "black hole" or "Bekenstein-Hawking".”(Wikipedia May 25, 2009) Witten (1998) has shown that the entropy of a black hole residing in the bulk Remembering Jacob G. W. Gibbons 21 The BlackHoleEntropy 33 4. Black hole entropy is a concept with geometric root but with many physical consequences. Jacob Bekenstein, Physicist Who Revolutionized Theory of Black Holes, Dies at 68 Jacob Bekenstein, third from right, who won the 2012 Wolf Prize in … : Lettere al Nuovo Cimento, 4, 737, (1972), Bekenstein J.D. I share some memories and offer a personal perspective on Jacob Bekenstein's legacy, focussing on black hole entropy and the Bekenstein bound. He is well - known for his fundamental contributions to the study of black hole thermodynamics. \], Consequently the horizon area is given by Even if the global state was pure and thus entropy free, this so reduced state will be a mixed one and have entropy associated with it. The physical content of the concept of black-hole entropy derives from the following generalized version of the second law: When common entropy goes down a black hole, the common entropy in the black-hole exterior plus the black-hole entropy never decreases. Bekenstein black hole area and entropy The NY Times obituary of Jacob Bekenstein says: acob Bekenstein, a physicist who prevailed in an argument with Stephen Hawking that revolutionized the study of black holes, and indeed the nature of space-time itself, died on Sunday in Helsinki, Finland, where he was to give a physics lecture. This notion reproduces formula (1) when the gravitational action is of first order in the curvature, but gives a modified formula for higher order gravity theories. \[\tag{1} Sad news reached Jen-Luc Piquant this morning via Jonathan Oppenheim's Twitter feed: physicist Jacob Bekenstein, a professor at the Hebrew University of Jerusalem, passed away last night. The physical content of the concept of black-hole entropy derives from the following generalized version of the second law: When common entropy goes down a black hole, the common entropy in the black-hole exterior plus the black-hole entropy never decreases. However, the hole's interior and contents are veiled to an exterior observer. dW = \Omega dJ + \Phi dQ\] Dr. Jacob D. Bekenstein (b. Enter Bekenstein and his seminal 1972 paper, which demonstrated that the entropy of a black hole is exactly proportional to the size of the event horizon around it. Metrics. Downloaded 7 times History. \], \[\tag{11} There are several ways to justify the concept of black hole entropy (Bekenstein 1972, 1973). Black hole entropy is the entropy of entanglement between degrees of freedom inside and outside the horizon. Black hole entropy is thermal entropy of the gas of quanta constituting the thermal atmosphere of the black hole. Thus by analogy one needs to associate entropy with a black hole . Just now this is just a relation between increments in mechanical and geometrical properties. Physical Review D™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. Thus it is reasonable that the black hole entropy should be a monotonic function of area, and it turns out to be simplest such function. Examples of this viewpoint are provided by Frolov and Novikov (1993) and by Mukhanov (2003). 1986). pressure, magnetic field, electric potential, etc. A black hole is usually formed from the collapse of a quantity of matter or radiation, both of which carry entropy. He has derived the Bekenstein-Hawking formula S=A/4 for the entropy of non-extremal black holes from loop quantum gravity, for all values of the Immirzi parameter. 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