Black hole entropy is equivalent to the thermal entropy of the radiation residing on the boundary of the spacetime containing the black hole. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. DOI:https://doi.org/10.1103/PhysRevD.7.2333. \[\tag{2} \). 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). 1, 34-40 (1977), Bekenstein, J. D.: Black-hole thermodynamics, Physics Today, 33, no. Jacob David Bekenstein was born in Mexico City on May 1, 1947. 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. Bekenstein also formulated the generalized second law of thermodynamics, black hole thermodynamics, for systems including black holes. Using conservative intuitive methods including time-old gedanken experiments, he discovered that black holes have thermodynamical properties such as entro… Bekenstein also formulated the generalized second law of thermodynamics, black hole thermodynamics , for systems including black holes. 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). For a black hole formed by collapse, the quantum field degrees of freedom external to the horizon should be entangled with those inside it. At the corresponding value of \(g\ ,\) string and black hole entropy are quite similar (see e.g. : 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. 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. Dr. Jacob D. Bekenstein (b. 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. 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. We give a brief overview of black hole entropy, covering main developments since Bekenstein’s original proposal. ‎Jacob Bekenstein, an Israeli physicist of the Hebrew University, Jerusalem, planted the seeds of a revolution of our understanding of space-time. This is particularly true for the first and second laws. \], \[\tag{11} 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 While this law may hold good for a system including a black hole, it is not informative in its original form. This page has been accessed 207,304 times. 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. A.: Physics Today, 24, no. This page was last modified on 25 April 2017, at 22:15. 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. 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. 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. There is some evidence that the unattainability statement of the third law is satisfied by black holes. Calculation (Bombelli et al. : Physical Review D, 9, 3292 (1974), Bekenstein J.D. Loading ... Close Figure Viewer. Jacob David Bekenstein hebr. Kerr-Newman black holes satisfying this condition are called extreme. 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. Use of the American Physical Society websites and journals implies that T dS = dE -dW\]. 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 verified by examples (Bekenstein 1973). 1. (GM/c^2)^2-(G^{1/2}Q^2/c^2)^2-(J/Mc)^2=0. Thus the Nernst-Simon statement of the third law fails for black holes. 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). 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. 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} There are a number of similarities between black-hole physics and thermodynamics. Metrics. 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. : Communications Mathematical Physics, 43, 199 (1975), Hawking S.W. Remembering Jacob G. W. Gibbons 21 The BlackHoleEntropy 33 4. Then we can analyze the null vector field on the horizon by Gauss theorem in curved space. Is it meaningful or desirable to associate entropy with it ? Dr. Hawking’s celebrated breakthrough resulted partly from a fight. Examples of this viewpoint are provided by Frolov and Novikov (1993) and by Mukhanov (2003). Onthe MicroscopicInterpretationofthe Bekenstein-Hawking Entropy J. M. Bardeen 11 3. This analogy suggests that black hole mass M might have a discrete spectrum. 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. Black hole entropy counts the number of internal states of matter and gravity. 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. Hawking had initially … Downloaded 7 times History. Because \(Mc^2\) is the hole's energy, equation (7) obviously looks like the first law for an ordinary thermodynamic system. We appreciate your continued effort and commitment to helping advance science, and allowing us to publish the best physics journals in the world. Black hole entropy is the entropy of entanglement between degrees of freedom inside and outside the horizon. 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. r=r_h\equiv GM/c^2+\sqrt{(GM/c^2)^2-(G^{1/2}Q/c^2)^2-(J/Mc)^2}. 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. 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. Unattainability statement: To bring a system to absolute zero temperature involves an infinite number of processes or steps. 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. 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