S_{BH}={A\over 4 L_{P}^2}={c^3 A\over 4 G \hbar}, Examples of this viewpoint are provided by Frolov and Novikov (1993) and by Mukhanov (2003). (GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2=0. All rights reserved. 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 See Off-Campus Access to Physical Review for further instructions. Kerr-Newman black holes satisfying this condition are called extreme. \Phi_{BH}\equiv Qr_h\Big(r_h^2+(J/Mc)^2\Big)^{-1}. In ordinary thermodynamics the second law requires that the entropy of a closed system shall never decrease, and shall typically increase as a consequence of generic transformations. The black hole entropy is proportional to its area A. A black hole is usually formed from the collapse of a quantity of matter or radiation, both of which carry entropy. (GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2=0. This has been verified by examples (Bekenstein 1973). JacobBekenstein and the DevelopmentofBlack Hole Thermodynamics R. M. Wald 3 2. Institute for Advanced Study, Princeton, NJ 08540, USA. Thus the Nernst-Simon statement of the third law fails for black holes. \], When near to equilibrium a thermodynamic system at temperature $$T$$ changes its state, the consequent increments of its energy $$E$$ and entropy $$S$$ are related by the first law of thermodynamics: 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. In thermodynamics one meets a similar situation: many internal microstates of a system are all compatible with the one observed (macro)state. Bekenstein, Jacob D. There are a number of similarities between black-hole physics and thermodynamics. 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). 1. Jacob D. Bekenstein's 121 research works with 18,523 citations and 2,683 reads, including: Statistics of black hole radiance and the horizon area spectrum 1, 34-40 (1977), Bekenstein, J. D.: Black-hole thermodynamics, Physics Today, 33, no. ‎Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. In 1972, Bekenstein was the first to suggest that black holes should have a well-defined entropy. Unattainability statement: To bring a system to absolute zero temperature involves an infinite number of processes or steps. There are a number of similarities between black-hole physics and thermodynamics. The atmosphere concept comes from Thorne and Zurek (1985) and 't Hooft (1985,1996); the last introduced the concept of a "brick wall" to keep the said atmosphere from contacting the horizon, and thus making the entropy infinite. 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. For Authors and Black Hole Entropy By |Jennifer Ouellette August 17, 2015 | The Bekenstein–Hawking entropy formula for a black hole. In 1972, Bekenstein was the first to suggest that black holes should have a well-defined entropy. This collection of seminal papers from PRD highlights research that remains central to developments today in particle physics, quantum field and string theory, gravitation, cosmology, and particle astrophysics. Black hole entropy is a concept with geometric root but with many physical consequences. Physical Review D™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. \], $$\tag{13} Here \(dW$$ is the work done on the system by exterior agents. : Physical Review D, 13, 191 (1976), Misner, C. W., Thorne, K. S. and Wheeler, J. This picture has been corroborated in the context of five-dimensional extreme black holes (Strominger and Vafa 1996). It will be the first law if black hole entropy is required to be a function of $$A$$ and of nothing else, so that $$dS_{BH}\propto dA$$ (Gour and Mayo 2001). This article appears in the following collections: The editors of the Physical Review journals have curated a collection of landmark papers on General Relativity to celebrate its centennial. A stationary black hole admits a similar relation (Bekenstein 1973). With the choice in equation (1) the black hole temperature $$T_{BH}$$ must be Caption. 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. Downloaded 7 times History. To address this, we have been improving access via several different mechanisms. He is well - known for his fundamental contributions to the study of black hole thermodynamics. T dS = dE -dW\]. To avoid violations, he found that he had to assume limitations on how close to the black hole’s horizon one could lower matter. Because $$Mc^2$$ is the hole's energy, equation (7) obviously looks like the first law for an ordinary thermodynamic system. Metrics. \Theta\, dA = d(Mc^2) -\Omega_{BH}\, dJ - \Phi_{BH}\, dQ\], $\tag{8} 1. \[\tag{4} Jacob David Bekenstein was born in Mexico City on May 1, 1947. : 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. Every object has some amount of entropy. Prof. Jacob Bekenstein, a Black Hole Pioneer and Hebrew University Theoretical Physicist, Has Died The Hebrew University of Jerusalem חתן פרס וולף: אני מרגיש יותר בנוח בעולם אם אני מבין למה דברים קורים 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.$, Consequently the horizon area is given by May 1, 1947, Mexico city) is the Micheal Polak Professor of Theoretical Physics at the Hebrew University of Jerusalem, Israel. This is particularly true for the first and second laws. Black hole entropy is a concept with geometric root but with many physical consequences. Note that a one-solar mass Schwarzschild black hole has an horizon area of the same order as the municipal area of Atlanta or Chicago. sufficiently slowly) reducing the string coupling constant In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. Both contributions were affirmed when Stephen Hawking (and, independently, Zeldovich and others) proposed the existence of Hawking radiationtwo years later. In ordinary thermodynamics the third law may be stated in two ways: From formula (11) it is clear that the black hole temperature 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. 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). Jacob Bekenstein, a physicist who prevailed in an argument with Stephen Hawking that revolutionized the study of black holes, and indeed the nature of … It turns out that $$\Omega_{BH}$$ is precisely the angular rotation frequency of the black hole in the sense that any test body dropped into it, as it approaches the horizon no matter where, ends up circumnavigating it at just this frequency. $\tag{11} Il est le premier à suggérer que les trous noirs ont une entropie et une température, il est donc le précurseur de la thermodynamique des trous noirs . \[\tag{7} 1997). Jacob David Bekenstein died of a heart attack on 16 August 2015 in Helsinki, Finland, where he was visiting to present a seminar. Conditions and any applicable This observation underscores the fact that one should not think of black hole entropy as the entropy that fell into the black hole when it was formed. 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. \Omega_{BH}\equiv (J/Mc)\Big(r_h^2+(J/Mc)^2\Big)^{-1}; Sign up to receive regular email alerts from Physical Review D. ISSN 2470-0029 (online), 2470-0010 (print). The AdS/CFT correspondence is a mapping between gravitational degrees of freedom of a certain spacetime and the matter (or field) degrees of freedom residing on its boundary. In ordinary statistical mechanics, the entropy $$S$$ is a measure of the multiplicity of microstates that hide behind one particular macrostate. to the above formula. 1986). $$\tag{13} and Page, D.N. At the corresponding value of \(g\ ,$$ string and black hole entropy are quite similar (see e.g. Using conservative intuitive methods including time-old gedanken experiments, he discovered that black holes have thermodynamical properties such as entro… Jacob David Bekenstein died of a heart attack on 16 August 2015 in Helsinki, Finland, where he was visiting to present a seminar. : Physical Review D, 12, 3077 (1975), Bombelli, L., Koul, R., Lee, J. and Sorkin, R.: Physical Review D, 34, 373 (1986), Bowick, M., Smolin, L. and Wijewardhana, L.C.R. Juan Maldacena; Juan Maldacena. Of course, if the entropy in the usual (chemist's) form is required, the above should be multiplied by Boltzmann's constant $$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\ ,$$ or I've known him well enough, especially from his Spring 2004 visit to Harvard when I talked to him many times (although less frequently than with the most important communication counterparts). Thus there are many possible internal states corresponding to that black hole. The reality of black hole temperature was brought home when Hawking showed (Hawking 1974, 1975) that a non-eternal black hole must spontaneously emit thermal radiation (Hawking radiation) with precisely this temperature (the original calculation was for $$J=0, Q=0\ ,$$ but it is now clear that equation (11) is valid for all $$J$$ and $$Q$$).$, $\tag{11} pressure, magnetic field, electric potential, etc. Use of the American Physical Society websites and journals implies that Bekenstein’s work on black holes, entropy, and thermodynamics initiated the field of black hole thermodynamics, which became the foundation for the science of quantum gravity. Sad news reached Jen-Luc Piquant this morning via Jonathan Oppenheim's Twitter feed: physicist Jacob Bekenstein, a professor at the Hebrew University of Jerusalem, passed away last night. Resources. Bekenstein showed that a fundamental limit on information density existed, the Bekenstein Bound and, like with a black hole's entropy, was … : Physical Review Letters, 93, 3902 (1993) (, Frolov, V. and Novikov, I.: Physical Review D, 48, 4545 (1993) (, Gour, G. and Mayo, A.M.: Physical Review D, 63, 064005 (2001) (, Hawking S.W. Zwiebach 2004).$, $\tag{4} Jacob David Bekenstein was born in Mexico City on May 1, 1947. Education Bekenstein received his undergraduate education in the Polytechnic University (now \Delta S_o +\Delta S_{BH} \geq 0. Jacob D. Bekenstein; There are a number of similarities between black-hole physics and thermodynamics. T_{BH}=4 L_P^2 \Theta ={ \hbar c\over 2\pi} {\sqrt{(GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2}\over r_h^2+(J/Mc)^2} COVID-19 has impacted many institutions and organizations around the world, disrupting the progress of research. From equations (1) and (3)-(4) it is clear that for $$T_{BH}=0$$ the black hole entropy is not only nonvanishing, but depends on $$(J/Mc)\ .$$ Now this last quantity is an analog of a thermodynamic intensive parameter. We here re-analyze an intriguing gedanken experiment which was designed by Bekenstein to challenge the GSL. If $$A$$ stands for the surface area of a black hole (area of the event horizon), then the black hole entropy, in dimensionless form, is given by the user has read and agrees to our Terms and \). And we hope you, and your loved ones, are staying safe and healthy. Black hole, Bekenstein bound, Hawking radiation, The first law of black hole thermodynamics, The generalized second law of thermodynamics, Status of the third law of black hole thermodynamics, \[\tag{1} Associating entropy with the black hole provides a handle on the thermodynamics. In physics, the Bekenstein bound (named after Jacob Bekenstein) is an upper limit on the entropy S, or information I, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximal amount of information required to perfectly describe a given physical system down to the quantum level. Black hole entropy is thermal entropy of the gas of quanta constituting the thermal atmosphere of the black hole. \), Institut de Physique Théorique, CEA & CNRS, Gif-sur-Yvette, France, Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopedia, Centro Atomico Bariloche, 8400-S.C. de Bariloche, Rio Negro, Argentina, http://www.scholarpedia.org/w/index.php?title=Bekenstein-Hawking_entropy&oldid=182595, Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. I summarize a number of fascinating recent developments that grew out of Bekenstein's pioneering contributions, from the Ryu-Takayanagi proposal to the Quantum Null Energy Condition. A special case of this is Boltzmann's famous formula $$S=\ln W$$ where $$W$$ stands for the number of equally probable microstates of a particular macrostate. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. Anti-deSitter spacetime equals that of thermal radiation of the fields residing on its boundary. 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. 2, 58-65 (2003). He was awarded the Wolf Prize in … 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. \Theta\, dA = d(Mc^2) -\Omega_{BH}\, dJ - \Phi_{BH}\, dQ$, where Public domain, via Wikimedia Commons. : The quantum mechanics of black holes, Scientific American, 236, no. 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. 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. In equations Metrics. Considerations of simplicity and consistency, and dimensional arguments indicate that the black-hole entropy is equal to the ratio of the black-hole area to the square of the Planck length times a dimensionless constant of order unity. 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). \], $\tag{3} Agreement. Quantum Gravity, 16, 3327 (1999) (, Frolov, V.P. Previous Figure Next Figure. \Theta\equiv c^4(2GA)^{-1}(r_h-GM/c^2); 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. : Communications Mathematical Physics, 43, 199 (1975), Hawking S.W. \[\tag{2} This increasing behavior is reminiscent of thermodynamic entropy of closed systems. Public domain, via Wikimedia Commons.$. For example, if an ordinary system falls into a black hole, the ordinary entropy becomes invisible to an exterior observer, so from her viewpoint, saying that ordinary entropy increases does not provide any insight: the ordinary second law is transcended. 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. ©2021 American Physical Society. Hawking had initially … 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. It is clear at the outset that black hole entropy should only depend on the observable properties of the black hole: mass, electric charge and angular momentum. Jacob D. Bekenstein, Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel. : Gen. Rel. The APS Physics logo and Physics logo are trademarks of the American Physical Society. Black hole entropy counts the number of internal states of matter and gravity. En 1973, Bekenstein fut le premier à suggérer que les trous noirs puissent avoir une entropie bien définie. Physics Today 68 (12). This is particularly true for the first and second laws. This is particularly true for the first and second laws. The subscript BH either stands for "black hole" or "Bekenstein-Hawking".”(Wikipedia May 25, 2009) A.: Physics Today, 24, no. Loading ... Close Figure Viewer. Black hole entropy is a conserved quantity connected with coordinate invariance of the gravitational action. 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. Large black holes in string theory 5 4.1 Five-dimensional black holes 6 4.1.1 D1-D5 wrapped on T4 ×S1 with compact momentum 6 4.1.2 Formal analysis by 5D supergravity 9 Robert M. Wald: (1 December 2015)"Jacob David Bekenstein". We here re-analyze an intriguing gedanken experiment which was designed by Bekenstein to challenge the GSL. Among his many honors, he received the Wolf Prize in 2012 and the American Physical Society’s Einstein Prize in 2015, both of which are often precursors of the Nobel Prize. 1972 ), 2470-0010 ( print ) the DevelopmentofBlack hole thermodynamics, black hole 's formation Bardeen! Opened to understanding of space-time entropy shall more than compensate for the and. Satisfied by black holes satisfying this condition are called extreme he is -... Advanced study, Princeton, NJ 08540, USA statement: the quantum mechanics of black hole plays. Satisfied by black holes particularly true for the first to suggest that black holes properties... Researchers now find themselves working away from their institutions and, thus may! The basis of a thermodynamic approach to black-hole Physics Institute for Advanced study, Princeton, NJ,. 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