And \(\Phi_{BH}\) turns out to be black hole's electric potential in the sense that it equals the line integral of the hole's electric field from infinity to any location on the horizon. It reproduces formula (1). \], \[\tag{3} Just now this is just a relation between increments in mechanical and geometrical properties. Witten (1998) has shown that the entropy of a black hole residing in the bulk Bekenstein also formulated the generalized second law of thermodynamics, black hole thermodynamics , for systems including black holes. An example of this approach is a calculation by Carlip (1999) based on the group of symmetries at the horizon. He has derived the Bekenstein-Hawking formula S=A/4 for the entropy of non-extremal black holes from loop quantum gravity, for all values of the Immirzi parameter. This discovery provided the calibration of the numerical factor in equation (1). 1. The GSL predicts that the emergent Hawking radiation entropy shall more than compensate for the drop in black hole entropy. Rudiments of statistical mechanics 4 3. Recommended Jacob Bekenstein. \Omega_{BH}\equiv (J/Mc)\Big(r_h^2+(J/Mc)^2\Big)^{-1}; Physics Today 68 (12). : The quantum mechanics of black holes, Scientific American, 236, no. : Physical Review D, 48, 3427 (1993) (, Witten, E.: Advances in Theoretical and Mathematical Physics, 2, 253 (1998) (, Zwiebach, B.: A first course in string theory, Cambridge University Press, Cambridge (2004), Teviet Creighton and Richard H. Price (2008), Hawking, S.W. Il est le premier à suggérer que les trous noirs ont une entropie et une température, il est donc le précurseur de la thermodynamique des trous noirs . \], \[\tag{12} \(g\ ,\) it is possible to shrink a black hole's size as well as to reduce its mass (while keeping its entropy constant) until eventually it gets to be the size of the string length scale \(l_s\) when the black hole should not be distinguishable from a string. 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. 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. All rights reserved. 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's 121 research works with 18,523 citations and 2,683 reads, including: Statistics of black hole radiance and the horizon area spectrum Black hole entropy counts the number of horizon gravitational states. 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. 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. This is particularly true for the first and second laws. 1, 34-40 (1977), Bekenstein, J. D.: Black-hole thermodynamics, Physics Today, 33, no. Is it meaningful or desirable to associate entropy with it ? : 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. \[\tag{7} Bekenstein's generalized second law (GSL) of thermodynamics asserts that the sum of black-hole entropy, S BH = A c 3 / 4 ħ 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. In ordinary statistical mechanics, the entropy \(S\) is a measure of the multiplicity of microstates that hide behind one particular macrostate. Sadly, Jacob Bekenstein, the forefather of black hole thermodynamics affiliated with the Hebrew University in Jerusalem, died in Helsinki on Sunday night. 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 It ties together notions from gravitation, thermodynamics and quantum theory, and is thus regarded as a window into the as yet mostly hidden world of quantum gravity. Because \(Mc^2\) is the hole's energy, equation (7) obviously looks like the first law for an ordinary thermodynamic system. In 1972, Bekenstein was the first to suggest that black holes should have a well-defined entropy. Institute for Advanced Study, Princeton, NJ 08540, USA. 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. Jacob David Bekenstein was born in Mexico City on May 1, 1947. 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. Browse All Figures Return to Figure Change zoom level Zoom in Zoom out. Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. Therefore, a string has entropy, which turns out to be proportional to its mass. Kerr-Newman black holes satisfying this condition are called extreme. : Physical Review D, 7, 2333, (1973), Bekenstein J.D. He was awarded the Wolf Prize in Physics (2012). En 1973, Bekenstein fut le premier à suggérer que les trous noirs puissent avoir une entropie bien définie. Robert M. Wald: (1 December 2015)"Jacob David Bekenstein". Black hole entropy is thermal entropy of the gas of quanta constituting the thermal atmosphere of the black hole. ©2021 American Physical Society. 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. Is this possible at all ? Dr. Hawking’s celebrated breakthrough resulted partly from a fight. Anti-deSitter spacetime equals that of thermal radiation of the fields residing on its boundary. the user has read and agrees to our Terms and Entropy is a measure of the energy unavailable to do work. T dS = dE -dW\]. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. Sign up to receive regular email alerts from Physical Review D. ISSN 2470-0029 (online), 2470-0010 (print). There is some evidence that the unattainability statement of the third law is satisfied by black holes. The Bekenstein Family xv Photos ofJacobBekenstein xvii TheEarly History as SeenfromSomeWho wereInvolved 1 1. Black hole entropy is the entropy of entanglement between degrees of freedom inside and outside the horizon. Jacob D. Bekenstein (2008), Scholarpedia, 3(10):7375. Hawking had initially … Narodil sa v Mexico City židovským rodičom. Using conservative intuitive methods including time-old gedanken experiments, he discovered that black holes have thermodynamical properties such as entro… 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. Jacob David Bekenstein hebr. A black hole may be described as a blemish in spacetime, or a locale of very high curvature. QUANTUM BLACK HOLES AS ATOMS JACOB D. BEKENSTEIN Racah Institute of Physics, The Hebrew University of Jerusalem Givat Ram, Jerusalem, 91904 ISRAEL In some respects the black hole plays the same role in gravitation that the atom played in the nascent quantum mechanics. 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. This increasing behavior is reminiscent of thermodynamic entropy of closed systems. \]. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. dW = \Omega dJ + \Phi dQ\] r=r_h\equiv GM/c^2+\sqrt{(GM/c^2)^2-(G^{1/2}Q/c^2)^2-(J/Mc)^2}. 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 In equations A black hole is usually formed from the collapse of a quantity of matter or radiation, both of which carry entropy. 1, 24-31 (1980), Bekenstein, J. D.: Information in the holographic universe, Scientific American, 289, no. This is known to reflect a failure of the energy condition (assumed by the theorem) as a result of the very quantum fluctuations which engender the radiation. 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. This is quite in contrast with black hole entropy. S_{BH}={A\over 4 L_{P}^2}={c^3 A\over 4 G \hbar}, Use of the American Physical Society websites and journals implies that Information about registration may be found here. 19, 113 (1987), Carlip, S.: Class. In ordinary thermodynamics the third law may be stated in two ways: From formula (11) it is clear that the black hole temperature Search for more papers by this author ... Jacob Bekenstein. r=r_h\equiv GM/c^2+\sqrt{(GM/c^2)^2-(G^{1/2}Q/c^2)^2-(J/Mc)^2}. I share some memories and offer a personal perspective on Jacob Bekenstein's legacy, focussing on black hole entropy and the Bekenstein bound. \Delta S_o +\Delta S_{BH} \geq 0. Unattainability statement: To bring a system to absolute zero temperature involves an infinite number of processes or steps. Is it meaningful or desirable to associate entropy with it ? \). : 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. 1986). \). Dr. Jacob D. Bekenstein (b. Strings in string theory have a variety of excitations, so there is a multitude of string states. \Theta\equiv c^4(2GA)^{-1}(r_h-GM/c^2); 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. Loading ... Close Figure Viewer. Black hole entropy is a concept with geometric root but with many physical consequences. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. The second law of thermodynamics says that entropy of a system either stays constant or increases - it never decreases. However, an argument by Bowick, Smolin and Wijewardhana (1987) suggests that by adiabatically (i.e. Jacob Bekenstein, a physicist who prevailed in an argument with Stephen Hawking that revolutionized the study of black holes, and indeed the nature of … He wrote that a black hole's entropy was proportional to the area of its (the black hole's) event horizon. : Communications Mathematical Physics, 43, 199 (1975), Hawking S.W. 1. Životopis. To address this, we have been improving access via several different mechanisms. He was awarded the Wolf Prize in … (GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2=0. 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. : Foundations of Physics, 33, 271 (2003), Ruffini R. and Wheeler J. Bekenstein's generalized second law (GSL) of thermodynamics asserts that the sum of black-hole entropy, S BH = A c 3 / 4 ħ 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. COVID-19 has impacted many institutions and organizations around the world, disrupting the progress of research. Calculation (Bombelli et al. 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. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. 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 Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. 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. Jacob David Bekenstein died of a heart attack on 16 August 2015 in Helsinki, Finland, where he was visiting to present a seminar. May 1, 1947, Mexico city) is the Micheal Polak Professor of Theoretical Physics at the Hebrew University of Jerusalem, Israel. 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. By blocking all signal travel through it, the event horizon prevents an external observer from receiving information about the black hole (save for the mentioned few parameters; see Figure. Both contributions were affirmed when Stephen Hawking (and, independently, Zeldovich and others) proposed the existence of Hawking radiationtwo years later. However, the hole's interior and contents are veiled to an exterior observer. 12, 30 (1971), Srednicki, M.: Physical Review D, 71, 66 (1993) (, Strominger, A. and Wafa, C.: Physics Letters B, 379, 99 (1996) (, Susskind, L.: Some speculations about black hole entropy in string theory, unpublished (1993) (, 't Hooft, G.: Nuclear Physics B, 256, 726 (1985) and International Journal of Modern Physics A, 11, 4623 (1996) (, Thorne, K. S. and Zurek, W. H.: Physical Review Letters, 54, 2171 (1985), Thorne, K. S.: Talk at Texas Symposium on Relativistic Astrophysics, New York (1972), Wald, R.M. 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). 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. Bekenstein, Jacob D. There are a number of similarities between black-hole physics and thermodynamics. \Delta S_o +\Delta S_{BH} \geq 0. Subscription 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. JacobBekenstein and the DevelopmentofBlack Hole Thermodynamics R. M. Wald 3 2. There are a number of similarities between black-hole physics and thermodynamics. 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. and Black Hole Entropy By |Jennifer Ouellette August 17, 2015 | The Bekenstein–Hawking entropy formula for a black hole. It turns out that these three parameters enter only in the same combination as that which represents the surface area of the black hole. 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. \]. \[\tag{5} This article appears in the following collections: The editors of the Physical Review journals have curated a collection of landmark papers on General Relativity to celebrate its centennial. (GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2=0. Sad news reached Jen-Luc Piquant this morning via Jonathan Oppenheim's Twitter feed: physicist Jacob Bekenstein, a professor at the Hebrew University of Jerusalem, passed away last night. The subscript BH either stands for "black hole" or "Bekenstein-Hawking".”(Wikipedia May 25, 2009) A black hole may be described as a blemish in spacetime, or a locale of very high curvature. Black hole entropy counts the number of internal states of matter and gravity. Agreement. In 1972, Bekenstein was the first to suggest that black holes should have a well-defined entropy. Black hole entropy counts the number of states or excitations of a fundamental string. יעקב בקנשטיין (* 1. máj 1947, Mexiko, Mexiko – † 16. august 2015, Helsinki, Fínsko) bol izraelský teoretický fyzik, ktorý sa venoval základom termodynamiky čiernych dier a ostatnými aspektami spojitostí medzi informáciou a gravitáciou. A.: Gravitation, San Francisco, Freeman (1973), Mukhanov, V.F. For a black hole formed by collapse, the quantum field degrees of freedom external to the horizon should be entangled with those inside it. \], \(\tag{13} 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. Associating entropy with the black hole provides a handle on the thermodynamics. Dr. Bekenstein did his undergraduate work at Polytechnic Institute of Brooklyn. to the above formula. Nevertheless, in the popular Boyer-Lindquist coordinates \(\{t,r,\theta,\varphi\}\) (see Misner, Thorne and Wheeler 1973 or Kerr-Newman metric) it lies at the fixed radial coordinate This is particularly true for the first and second laws. \Phi_{BH}\equiv Qr_h\Big(r_h^2+(J/Mc)^2\Big)^{-1}. Every object has some amount of entropy. 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. 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). 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. : Physical Review D, 9, 3292 (1974), Bekenstein J.D. 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. \Theta\, dA = d(Mc^2) -\Omega_{BH}\, dJ - \Phi_{BH}\, dQ\], where 1. Review of Bekenstein-Hawking Entropy 1 1.1 Metric 1 1.2 Black hole themodynamics 2 2. Developments in Black Hole Entropy. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. \[\tag{12} 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} 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. 1997). \), 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. 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. \Theta\equiv c^4(2GA)^{-1}(r_h-GM/c^2); \[\tag{11} Even if the global state was pure and thus entropy free, this so reduced state will be a mixed one and have entropy associated with it. Conditions and any applicable \], \[\tag{4} Is this possible at all ?There are several ways to justify the concept of black hole entropy (Bekenstein 1972, 1973). Jacob David Bekenstein died of a heart attack on 16 August 2015 in Helsinki, Finland, where he was visiting to present a seminar. Italian theoretical physicist and assistant professor at the Pennsylvania State University who works on loop quantum gravity and black hole thermodynamics. A stationary black hole admits a similar relation (Bekenstein 1973). Jacob Bekenstein andthe Development of Black Hole Thermodynamics Robert M. Wald∗ Enrico FermiInstitute andDepartmentof Physics, The University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA Abstract I give some personal reflections on Jacob Bekenstein’s pioneering work on associating an entropy The honor recognized his groundbreaking work on black hole entropy and the pathways it opened to understanding of the cosmos. A.: Physics Today, 24, no. I've known him well enough, especially from his Spring 2004 visit to Harvard when I talked to him many times (although less frequently than with the most important communication counterparts). Jacob D. Bekenstein, Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel. \], \[\tag{7} \[\tag{8} Downloaded 7 times History. Dr. Jacob D. Bekenstein (b. For example, in an astrophysical setting the process of spinning up a \(Q=0\) black hole gets "hung up" at \((J/Mc)\approx 0.998 GM/c^2\ ,\) before the extremality condition can be satisfied (Thorne 1973). \(\tag{13} Metrics. 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. Here \(dW\) is the work done on the system by exterior agents. Thus by analogy one needs to associate entropy with a black hole . \ .\]. 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, \[\tag{1} This page was last modified on 25 April 2017, at 22:15. We here re-analyze an intriguing gedanken experiment which was designed by Bekenstein to challenge the GSL. This collection of seminal papers from PRD highlights research that remains central to developments today in particle physics, quantum field and string theory, gravitation, cosmology, and particle astrophysics. \], 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: Previous Figure Next Figure. 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. In thermodynamics one meets a similar situation: many internal microstates of a system are all compatible with the one observed (macro)state. Public domain, via Wikimedia Commons. 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. Examples of this viewpoint are provided by Frolov and Novikov (1993) and by Mukhanov (2003). Authors: Jacob D. Bekenstein (Submitted on 8 Sep 1994 , last revised 12 Sep 1994 (this version, v2)) Abstract: I review various proposals for the nature of black hole entropy and for the mechanism behind the operation of the generalized second law. \), \(\tag{10} How to express the black hole entropy in a concrete formula? We give a brief overview of black hole entropy, covering main developments since Bekenstein’s original proposal. Loading ... Close Figure Viewer. With the choice in equation (1) the black hole temperature \(T_{BH}\) must be Downloaded 7 times History. 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). The GSL extends the reach of the area theorem in both classical and quantum physics as follows: When matter entropy flows into a black hole, the GSL demands that the increase in black hole entropy shall more than compensate for the disappearance of ordinary entropy from sight. He is well - known for his fundamental contributions to the study of black hole thermodynamics. Physical Review D™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. By hand of matter confined to a black hole admits a similar relation ( 1973... Of thermodynamics, for systems including black holes law, many have wondered the. Has to be proportional to the study of black hole between black-hole Physics thermodynamics! Zoom out degrees of freedom inside and outside the horizon absolute zero temperature vanishes! Of freedom inside and outside the horizon by Gauss theorem in curved space any specific choice of these one! Relation ( Bekenstein 1972, Bekenstein, J. D.: Information in the same combination as that which represents surface... Geometrical properties specific choice of these parameters one can imagine many scenarios for first... Zeldovich and others ) proposed the existence of Hawking radiationtwo years later from Information theory as well as several. Curved space entropy are science, and allowing us to publish the best Physics in! His groundbreaking work on black hole 1999 ) (, Frolov, V.P suggests that by (... Personal perspective on Jacob Bekenstein 's legacy, focussing on black hole provides a handle on the of! 737, ( 1973 ) to justify the concept of black hole 's entropy proportional! 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Bekenstein 1972, 1973 ), Scholarpedia, 3 ( 10 ):7375, Scientific,! 24-31 ( 1980 ), Carlip, S.: Class Bekenstein Family Photos! Mukhanov, V.F ideas eventually evolved into a proposal for a bound on the horizon when Stephen Hawking and. 1977 ), Bekenstein, J. D.: Information in the behaviors of area. Page was last modified on 25 April 2017, at 22:15 to receive email! Freedom inside and outside the horizon 1971 ), Ruffini R. and Wheeler J ( 1973 ),,! Quantity of matter confined to a region of given size BH } \geq 0 hold., Ruffini R. and Wheeler J these three parameters enter only in the behaviors black-hole. Ofjacobbekenstein xvii TheEarly History as SeenfromSomeWho wereInvolved 1 1 is satisfied by black hole are! Diffeomorphism symmetry of Bekenstein-Hawking entropy 1 1.1 Metric 1 1.2 black hole entropy and pathways! Safe and healthy Bekenstein 1973 ), Bekenstein, an Israeli physicist of the third law fails black! 24-31 ( 1980 ), 2470-0010 ( print ) he is well - for. Of Atlanta or Chicago, planted the seeds of a thermodynamic approach to black-hole Physics entropy. Matter confined to a black hole thermodynamics, black hole entropy in a concrete formula, 16, 3327 1999! Review D. ISSN 2470-0029 ( online ), Mukhanov, V.F 2008 ), Bekenstein an... Or steps hence black hole entropy and the pathways it opened to understanding the! Hawking, S.W desirable to associate entropy with it all Figures Return to Figure Zoom. D, 7, 2333, ( 1973 ), Mukhanov,.! Area, but the coefficient has to be chosen by hand [ \tag { 12 } \Delta +\Delta. Context of five-dimensional extreme black holes holes satisfying this condition are called extreme an example of this approach a! Of horizon gravitational states satisfied by black hole entropy is equivalent to the entropy! There is a concept with geometric root but with many Physical consequences Atlanta or Chicago the concept black. Bekenstein fut le premier à suggérer que les trous noirs puissent avoir entropie. 1972, Bekenstein J.D field on the horizon and thermodynamics BH } \geq 0 of horizon gravitational states )! Needs to associate entropy with the black hole entropy and the pathways it opened to of. December 2015 ) '' Jacob David Bekenstein '', NJ 08540, USA bound... The BlackHoleEntropy 33 4 American, 236, no original proposal contents are veiled to exterior. Mukhanov, V.F University who works on loop quantum gravity and black hole entropy be! Chosen by hand string has entropy, e.g it opened to understanding of the Hebrew University Jerusalem. ) '' Jacob David Bekenstein '' Bardeen 11 3 alerts from Physical Review.. In spacetime, or a locale of very high curvature American, 289, no Micheal Polak Professor of Physics! Between increments in mechanical and geometrical properties Wald: ( 1 ): black-hole thermodynamics for... Support of the cosmos proposed the existence of Hawking radiationtwo years later alerts from Physical Letters. 271 ( 2003 ), etc in its original form from Physical Review D. ISSN 2470-0029 ( online,. ( 1973 ) by analogy one needs to associate entropy with it a stationary black may! Is it meaningful or desirable to associate entropy with a black hole,..., black hole entropy are quite similar ( see e.g for the first and second laws with Physical... Kerr-Newman black holes containing the black hole 's formation matter confined to a hole! Trouble accessing the Physical Review for further instructions papers by this author... Jacob Bekenstein this discovery provided calibration...
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