\Theta\, dA = d(Mc^2) -\Omega_{BH}\, dJ - \Phi_{BH}\, dQ\], where In ordinary thermodynamics the third law may be stated in two ways: From formula (11) it is clear that the black hole temperature This picture has been corroborated in the context of five-dimensional extreme black holes (Strominger and Vafa 1996). 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 increasing behavior is reminiscent of thermodynamic entropy of closed systems. \[\tag{5} 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 hole entropy is the entropy of entanglement between degrees of freedom inside and outside the horizon. 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. 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 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. Is this possible at all ?There are several ways to justify the concept of black hole entropy (Bekenstein 1972, 1973). He was awarded the Wolf Prize in … : Physical Review D, 7, 2333, (1973), Bekenstein J.D. 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. S_{BH}={A\over 4 L_{P}^2}={c^3 A\over 4 G \hbar}, 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. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. Black hole entropy is a concept with geometric root but with many physical consequences. Loading ... Close Figure Viewer. \[\tag{6} \], \[\tag{7} 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 2, 58-65 (2003). 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. Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. 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. Many researchers now find themselves working away from their institutions and, thus, may have trouble accessing the Physical Review journals. Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. Bekenstein also formulated the generalized second law of thermodynamics, black hole thermodynamics, for systems including black holes. Associating entropy with the black hole provides a handle on the thermodynamics. Sadly, Jacob Bekenstein, the forefather of black hole thermodynamics affiliated with the Hebrew University in Jerusalem, died in Helsinki on Sunday night. Public domain, via Wikimedia Commons. 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. 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. Jacob D. Bekenstein; There are a number of similarities between black-hole physics and thermodynamics. The black hole entropy is proportional to its area A. : 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. Strings in string theory have a variety of excitations, so there is a multitude of string states. Jacob David Bekenstein was born in Mexico City on May 1, 1947. Jacob David Bekenstein died of a heart attack on 16 August 2015 in Helsinki, Finland, where he was visiting to present a seminar. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. To avoid violations, he found that he had to assume limitations on how close to the black hole’s horizon one could lower matter. Jacob D. Bekenstein (2008), Scholarpedia, 3(10):7375. 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. 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). He is well - known for his fundamental contributions to the study of black hole thermodynamics. 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. Robert M. Wald: (1 December 2015)"Jacob David Bekenstein". Is it meaningful or desirable to associate entropy with it ? The subscript BH either stands for "black hole" or "Bekenstein-Hawking".”(Wikipedia May 25, 2009) \Delta S_o +\Delta S_{BH} \geq 0. 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. The GSL predicts that the emergent Hawking radiation entropy shall more than compensate for the drop in black hole entropy. 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. All rights reserved. Use of the American Physical Society websites and journals implies that Calculation (Bombelli et al. Jacob D. Bekenstein, Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel. 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} \ .\]. Those ideas eventually evolved into a proposal for a bound on the entropy-to-energy ratio of matter confined to a region of given size. \[\tag{8} 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. 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} 1986). \[\tag{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. 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. ↑ Jacob Bekenstein, Black Hole Pioneer and Hebrew University Physicist, Has Died Loading ... Close Figure Viewer. \(\tag{13} 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. 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 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. Using conservative intuitive methods including time-old gedanken experiments, he discovered that black holes have thermodynamical properties such as entro… 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 ↑Jacob Bekenstein, Black Hole Pioneer and Hebrew University Physicist, Has Died ↑ Jennifer Ouellette, « In Memoriam: Jacob Bekenstein (1947-2015) and Black Hole Entropy », sur blogs.scientificamerican.com, 17 août 2015 : Lettere al Nuovo Cimento, 4, 737, (1972), Bekenstein J.D. 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. Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. 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. : Gen. Rel. \[\tag{4} Black hole entropy is thermal entropy of the gas of quanta constituting the thermal atmosphere of the black hole. Institute for Advanced Study, Princeton, NJ 08540, USA. (GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2=0. Dr. Hawking’s celebrated breakthrough resulted partly from a fight. This discovery provided the calibration of the numerical factor in equation (1). \[\tag{12} to the above formula. Browse All Figures Return to Figure Change zoom level Zoom in Zoom out. We here re-analyze an intriguing gedanken experiment which was designed by Bekenstein to challenge the GSL. Anti-deSitter spacetime equals that of thermal radiation of the fields residing on its boundary. He was awarded the Wolf Prize in Physics (2012). 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. Nernst-Simon statement: The entropy of a system at absolute zero temperature either vanishes or becomes independent of the intensive thermodynamic parameters, e.g. Because \(Mc^2\) is the hole's energy, equation (7) obviously looks like the first law for an ordinary thermodynamic system. it participates in the second law, many have wondered what the microstates that are counted by black hole entropy are. Jacob Bekenstein, a physicist who prevailed in an argument with Stephen Hawking that revolutionized the study of black holes, and indeed the nature of … 1997). May 1, 1947, Mexico city) is the Micheal Polak Professor of Theoretical Physics at the Hebrew University of Jerusalem, Israel. Resources. Thus there are many possible internal states corresponding to that black hole. To address this, we have been improving access via several different mechanisms. Italian theoretical physicist and assistant professor at the Pennsylvania State University who works on loop quantum gravity and black hole thermodynamics. I had a look at Jacob Bekenstein's 1973 Physical Review D paper "Black holes and entropy" for the answer to my question about Susskind's presentation of the Bekenstein derivation of the formula stating that black hole entropy is proportional to horizon area. Thus by analogy one needs to associate entropy with a black hole . \Phi_{BH}\equiv Qr_h\Big(r_h^2+(J/Mc)^2\Big)^{-1}. \], \[\tag{12} S_{BH}={A\over 4 L_{P}^2}={c^3 A\over 4 G \hbar}, Sign up to receive regular email alerts from Physical Review D. ISSN 2470-0029 (online), 2470-0010 (print). 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. To an external observer the last are not accessible, so the meaningful state would be the one from which internal degrees of freedom have been traced out (removed). This page was last modified on 25 April 2017, at 22:15. \], \[\tag{11} I share some memories and offer a personal perspective on Jacob Bekenstein's legacy, focussing on black hole entropy and the Bekenstein bound. Juan Maldacena; Juan Maldacena. 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. 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 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. 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