$\tag{7} 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. 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. This is quite in contrast with black hole entropy. 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} At the corresponding value of $$g\ ,$$ string and black hole entropy are quite similar (see e.g. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. Caption. In ordinary thermodynamics the third law may be stated in two ways: From formula (11) it is clear that the black hole temperature \Theta\equiv c^4(2GA)^{-1}(r_h-GM/c^2); Strings in string theory have a variety of excitations, so there is a multitude of string states. There is some evidence that the unattainability statement of the third law is satisfied by black holes. 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. 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. \[\tag{2} This is particularly true for the first and second laws. Public domain, via Wikimedia Commons. Agreement. Information about registration may be found here. 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 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 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 Here $$dW$$ is the work done on the system by exterior agents. May 1, 1947, Mexico city) is the Micheal Polak Professor of Theoretical Physics at the Hebrew University of Jerusalem, Israel. Jacob Bekenstein, Physicist Who Revolutionized Theory of Black Holes, Dies at 68 Jacob Bekenstein, third from right, who won the 2012 Wolf Prize in … 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. 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. Using conservative intuitive methods including time-old gedanken experiments, he discovered that black holes have thermodynamical properties such as entro… 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. There are a number of similarities between black-hole physics and thermodynamics. Black hole entropy is thermal entropy of the gas of quanta constituting the thermal atmosphere of the black hole. \[\tag{4} Using conservative intuitive methods including time-old gedanken experiments, he discovered that black holes have thermodynamical properties such as entro… 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 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. pressure, magnetic field, electric potential, etc. And we hope you, and your loved ones, are staying safe and healthy. We here re-analyze an intriguing gedanken experiment which was designed by Bekenstein to challenge the GSL. 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. The validity of this version of the second law is supported by an argument from information theory as well as by several examples. Black hole entropy is a concept with geometric root but with many physical consequences. and Page, D.N. Jacob David Bekenstein died of a heart attack on 16 August 2015 in Helsinki, Finland, where he was visiting to present a seminar. For the most general type of stationary black hole, the Kerr-Newman black hole (rotating black hole), the hole's parameters are mass $$M\ ,$$ electric charge $$Q$$ and angular momentum $$J\ ,$$ and the horizon is no longer spherical. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. This analogy suggests that black hole mass M might have a discrete spectrum. ‎Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. 1986, Srednicki 1993) shows that this entanglement entropy is proportional to the horizon area, just as required to explain black hole entropy, but the coefficient is ultraviolet divergent and thus requires renormalization by physical arguments. the user has read and agrees to our Terms and \[\tag{8} Black hole entropy is the entropy of entanglement between degrees of freedom inside and outside the horizon. Black hole entropy is a concept with geometric root but with many physical consequences.$. Bekenstein's generalized second law (GSL) of thermodynamics asserts that the sum of black-hole entropy, S BH = A c 3 / 4 ħ G (here A is the black-hole surface area), and the ordinary entropy of matter and radiation fields in the black-hole exterior region never decreases. Both contributions were affirmed when Stephen Hawking (and, independently, Zeldovich and others) proposed the existence of Hawking radiationtwo years later. In thermodynamics one meets a similar situation: many internal microstates of a system are all compatible with the one observed (macro)state. T dS = dE -dW\]. 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. 1, 24-31 (1980), Bekenstein, J. D.: Information in the holographic universe, Scientific American, 289, no. Figure 1: The Bekenstein-Hawking entropy is the entropy ascribed to a black hole. He wrote that a black hole's entropy was proportional to the area of its (the black hole's) event horizon. Then we can analyze the null vector ﬁeld on the horizon by Gauss theorem in curved space. Examples of this viewpoint are provided by Frolov and Novikov (1993) and by Mukhanov (2003). May 1, 1947, Mexico city) is the Micheal Polak Professor of Theoretical Physics at the Hebrew University of Jerusalem, Israel. 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. and Black Hole Entropy By |Jennifer Ouellette August 17, 2015 | The Bekenstein–Hawking entropy formula for a black hole. This page was last modified on 25 April 2017, at 22:15. Bekenstein J.D. Is this possible at all ?There are several ways to justify the concept of black hole entropy (Bekenstein 1972, 1973). 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. Black hole entropy counts the number of horizon gravitational states. $\tag{6} Thus there are many possible internal states corresponding to that black hole. Conditions and any applicable$, $$\tag{9} 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. Dr. Jacob D. Bekenstein (b. \], Consequently the horizon area is given by Quantum Gravity, 16, 3327 (1999) (, Frolov, V.P. While this law may hold good for a system including a black hole, it is not informative in its original form. 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). I share some memories and offer a personal perspective on Jacob Bekenstein's legacy, focussing on black hole entropy and the Bekenstein bound. Jacob David Bekenstein was born in Mexico City on May 1, 1947. This picture has been corroborated in the context of five-dimensional extreme black holes (Strominger and Vafa 1996). Jacob Bekenstein in the early 1970’s: “What would happen if you poured a hot cup of tea into a black hole?” This has led to Bekenstein’s 1973 paper (4842 citations) “There are a number of similarities between black-hole physics and thermodynamics. ‎Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. Since black hole entropy plays a role quite analogous to that of ordinary entropy, e.g. $\tag{3}$, where \(L_P$$ stands for the Planck length $$G\hbar/c^3$$ while $$G, \hbar$$ and $$c$$ denote, respectively, Newton's gravity constant, the Planck-Dirac constant ($$h/(2\pi)$$) and the speed of light. For example, if an ordinary system falls into a black hole, the ordinary entropy becomes invisible to an exterior observer, so from her viewpoint, saying that ordinary entropy increases does not provide any insight: the ordinary second law is transcended. Of course, if the entropy in the usual (chemist's) form is required, the above should be multiplied by Boltzmann's constant $$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\ ,$$ or A black hole is When the system is one rotating with angular frequency $$\Omega$$ and charged up to electric potential $$\Phi$$, the changes in its angular momentum $$J$$ and charge $$Q$$ contribute the work \], $\tag{7} Bekenstein's generalized second law (GSL) of thermodynamics asserts that the sum of black-hole entropy, S BH = A c 3 / 4 ħ G (here A is the black-hole surface area), and the ordinary entropy of matter and radiation fields in the black-hole exterior region never decreases. A.: Physics Today, 24, no. 2, 58-65 (2003). r=r_h\equiv GM/c^2+\sqrt{(GM/c^2)^2-(G^{1/2}Q/c^2)^2-(J/Mc)^2}.$. Dr. Bekenstein did his undergraduate work at Polytechnic Institute of Brooklyn. 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 : 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. Metrics. 1986). : Gen. Rel. 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. 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 . Physical Review D™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. (GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2=0. 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. Downloaded 7 times History. Is it meaningful or desirable to associate entropy with it ? 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 $$Q$$). Search for more papers by this author ... Jacob Bekenstein. Thermodynamic entropy quantifies the said multiplicity. 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. This discovery provided the calibration of the numerical factor in equation (1). See Off-Campus Access to Physical Review for further instructions. The second law of thermodynamics says that entropy of a system either stays constant or increases - it never decreases. : Foundations of Physics, 33, 271 (2003), Ruffini R. and Wheeler J. 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. Sadly, Jacob Bekenstein, the forefather of black hole thermodynamics affiliated with the Hebrew University in Jerusalem, died in Helsinki on Sunday night. vanishes when $\tag{11} it participates in the second law, many have wondered what the microstates that are counted by black hole entropy are. Loading ... Close Figure Viewer. \Delta S_o +\Delta S_{BH} \geq 0. This page has been accessed 207,304 times. Associating entropy with the black hole provides a handle on the thermodynamics. Use of the American Physical Society websites and journals implies that \Theta\, dA = d(Mc^2) -\Omega_{BH}\, dJ - \Phi_{BH}\, dQ$, where A stationary black hole admits a similar relation (Bekenstein 1973). It turns out that these three parameters enter only in the same combination as that which represents the surface area of the black hole. In 1972, Bekenstein was the first to suggest that black holes should have a well-defined entropy. ↑ Jacob Bekenstein, Black Hole Pioneer and Hebrew University Physicist, Has Died 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. Jacob David Bekenstein hebr. 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. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. 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). The honor recognized his groundbreaking work on black hole entropy and the pathways it opened to understanding of the cosmos. 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. Anti-deSitter spacetime equals that of thermal radiation of the fields residing on its boundary. With the choice in equation (1) the black hole temperature $$T_{BH}$$ must be Jacob Bekenstein, a physicist who prevailed in an argument with Stephen Hawking that revolutionized the study of black holes, and indeed the nature of … 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). \Delta S_o +\Delta S_{BH} \geq 0. 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. \Phi_{BH}\equiv Qr_h\Big(r_h^2+(J/Mc)^2\Big)^{-1}. 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, Jacob D. There are a number of similarities between black-hole physics and thermodynamics. DOI:https://doi.org/10.1103/PhysRevD.7.2333. Education Bekenstein received his undergraduate education in the Polytechnic University (now Public domain, via Wikimedia Commons. dW = \Omega dJ + \Phi dQ\] Jacob David Bekenstein was born in Mexico City on May 1, 1947. There are several ways to justify the concept of black hole entropy (Bekenstein 1972, 1973). A.: Gravitation, San Francisco, Freeman (1973), Mukhanov, V.F. \). Metrics. Thus the Nernst-Simon statement of the third law fails for black holes. Previous Figure Next Figure. 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. 1. Review of Bekenstein-Hawking Entropy 1 1.1 Metric 1 1.2 Black hole themodynamics 2 2. Recommended Jacob Bekenstein. 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. A black hole is usually formed from the collapse of a quantity of matter or radiation, both of which carry entropy. 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. Rudiments of statistical mechanics 4 3. 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. to the above formula. He was awarded the Wolf Prize in Physics (2012). Black hole entropy counts the number of states or excitations of a fundamental string. \], \[\tag{3} We give a brief overview of black hole entropy, covering main developments since Bekenstein’s original proposal. Jacob D. Bekenstein (2008), Scholarpedia, 3(10):7375. 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 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. 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. Entropy is a measure of the energy unavailable to do work. Nernst-Simon statement: The entropy of a system at absolute zero temperature either vanishes or becomes independent of the intensive thermodynamic parameters, e.g. 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. Bekenstein also formulated the generalized second law of thermodynamics, black hole thermodynamics , for systems including black holes. (GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2=0. 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. An example of this approach is a calculation by Carlip (1999) based on the group of symmetries at the horizon. 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). Jacob D. Bekenstein; There are a number of similarities between black-hole physics and thermodynamics. In higher-dimensional space, the Bekenstein entropy formula is S= A 4GD (1.12) 2The proof uses the fact that the black hole horizon is generated by the null geodesics without future end points [10]. 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