black holes and entropy bekenstein
. Download Citation | Black hole entropy and the Bekenstein bound | I share some memories and offer a personal perspective on Jacob Bekenstein's legacy, focussing on black hole entropy and the . The classical laws of black hole mechanics together with the formula for the temperature of Hawking radiation allow one to identify a quantity associated with black holes — namely A/4 in general relativity — as playing the mathematical role of entropy.The apparent validity of the GSL provides strong evidence that this quantity truly is the physical entropy of a black hole. Por . In this note we have applied directly the Shannon formula for information theory entropy to derive the Black Hole (Bekenstein-Hawking) entropy. 10.8) where Planck's length is the denominator to Wheeler, who spoke of using Planck's length in conversation with Bekenstein on April 2, 1971. This is particularly true for the first and second laws. Black Hole Entropy: • Bekenstein and Hawking: event horizons have entropy! reproduce the entropy of all black holes, but this argument does not reproduce the entropy exactly. DOI: 10.1103/Physrevd.7.949 : 1: 1973: Bekenstein JD. In classical thermodynamics entropy is always supposed to be an extensive quantity, so S ∼ M. But the black hole entropy S B H ∼ M 2 is . Hot deals; Introduction. Bekenstein's 1972 proposal that black holes carry entropy Bek72 takes up four very small pages in a now extinct journal. Quantum entropy of a black hole is a quantum generalization of the celebrated Bekenstein-Hawking area formula. In this kind of cyclic scenario, there is no big crunch and no chaotic mixmaster behavior. It can be readily demonstrated that Bekenstein-Hawking black hole entropy is non-extensive, while the Hawking and the Unruh temperatures are non-intensive. D 9, 3292 (1974). In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. The black-hole entropy is proportional to the area of its event horizon . Home; Our Products; About Us; Our Team; Contact; Order Now. In ( perturbative) string theory the Bekenstein-Hawking entropy associated to a macroscopic black hole finds an explanation as follows: The black hole spacetime is regarded as a strongly coupled condensate of string states ( closed strings, carrying gravity ). After a brief review of the elements of the theory of information, we discuss black . By Jennifer Ouellette on August 17, 2015. Indeed, through Bekenstein bound, [4], one can see that the black hole entropy, as described by the area law, is the maximal entropy that can be achieved and this was the main hint that led to the holographic principle, [5]. This is accurate. Bekenstein (1974) J. D. Bekenstein, Phys. Quantum information is entangled, all the information accumulated inside the black hole is conserved after the evaporation of the black hole. As an explicit example, we study near extremal Banados-Teitelboim-Zanelli black holes and derive this claim from AdS{sub 3}/CFT{sub 2}. The Bekenstein-Hawking entropy is a statement about the gravitational entropy of a system. 752. [1, 2] due to the "no hair" theorems leading to their universal characters, but at the same time, they are probably one the most complex systems if one tries to understand (in a statistical mechanical way) the microscopic degrees . Another black hole mystery is the origin of Bekenstein entropy and the quantum mechanism of information storage and processing by a black hole. Enter the email address you signed up with and we'll email you a reset link. Hot deals. Besides, we obtain the mass, the temperature, and the entropy of the q-deformed quantum Schwarzschild black hole. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. The scaling of Bekenstein entropy as the horizon area, S ∼ L 2 / L P 2, creates the impression that the horizon is a union of N Planck-size pixels each housing a distinguishable degree of freedom that . Extraction of energy and charge from a black hole Physical Review D. 7: 949-953. black hole formula by ramanujan. Credit: Public domain, via Wikimedia Commons. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. Download: . BEKENSTEIN-HAWKING BLACK HOLE ENTROPY The Bekenstein-Hawking black hole entropy equation is A hG c k S B 2 π 3 = , (1) where S is entropy, c is the speed of light in vacuum, kB is Boltzmann's constant, h is Planck's constant, G is the universal constant of gravitation, and A is the area of the It ranks as one of the most important physics papers of the 20th century. But if black holes had entropy, they would have to emit radiation (which was thought impossible at the time). Another black hole mystery is the origin of Bekenstein entropy and the quantum mechanism of information storage and processing by a black hole. Yup. . Submission history Bekenstein, Jacob D. There are a number of similarities between black-hole physics and thermodynamics. I share some memories and offer a personal perspective on Jacob Bekenstein's legacy, focussing on black hole entropy and the Bekenstein bound. One looks for a corresponding weakly-coupled background for . In this case, the horizon area is given by. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. 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. This is much greater than the entropy of the matter that collapsed to form it: Thermal radiation has the highest entropy of ordinary matter, but a ball of thermal . 2. horizons. In 1973, Stephen Hawking ran calculations that showed that black holes would indeed create and emit particles. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. The generalised second law inspired Bekenstein to a little thought experiment which gave rise to the Bekenstein bound on information. See Page 1. as its quantization requires further study. Black-hole physics seems to provide at least two ways in which the second law of thermodynamics may be transcended or violated: a) Let an observer drop or lower a package of entropy into a black hole; the entropy of the exterior world decreases. Its volume doesn't work because there's . • quantum gravity provides a fundamental scale. "Black-hole dynamics has many points of resemblance with thermodynamics. An important black hole observable is the Bekenstein-Hawking (BH) entropy, which is proportional to the area of the event horizon, SBH = Ah / (4 G ). 2. horizon. Quantum information is entangled, all the information accumulated inside the black hole is conserved after the evaporation of the black hole. Download and reference "Black Holes And Entropy" by J. Bekenstein on Citationsy The temperature is inversely proportional to the mass: K, where g, the Planck mass. With 6 equations and less than 1500 words, it makes for an exceptionally quick and rewarding read. A solar-mass black hole has SBH ∼ 1077k. Categories. After a brief review of the elements of the theory of information, we discuss black . A = 4 π r s 2 = 16 π ( G c 2) 2 M 2. and the black hole entropy is therefore proportional to the mass of the black hole M squared: S B H = 4 π k B G ℏ c M 2. Wow. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. Our analysis is semi-classical in nature since we . ( 7)and(8)showthatsuchacorrespondence is consistent only if the black hole entropy has the Bekenstein-Hawking value, and endow . The quantum mass spectrum of the Kerr black hole Lettere Al Nuovo Cimento Series 2. PIPE • VALVES • FITTINGS • PLUMBING • INDUSTRIAL • HVAC/R • ELECTRICAL. depends only on the total horizon area--also a . Origins Bekenstein derived the bound from heuristic arguments involving black holes. The black hole entropy can be obtained through number of ways. 2 RINDLER SPACE 22 Figure 2: The von Neumann entropy versus time for an evaporating black hole according to Hawking and Page 3 Current Price Index; Current Price Sheet We find an upper bound on the mass of a black hole/white hole pair. The scaling of Bekenstein entropy as the horizon area, S ∼ L 2 / L P 2, creates the impression that the horizon is a union of N Planck-size pixels each housing a distinguishable degree of freedom that . sonoma academy calendar; why are my bluetooth headphones connected but not working; black hole formula by ramanujan The basic physical reasoning is that the area of its horizon is the only physical geometry-related quantity that a black hole can actually have. The fact that the black-hole entropy is also the maximal entropy that can be obtained by the Bekenstein bound (wherein the Bekenstein bound becomes an equality) was the main observation that led to the holographic principle. According to the Bekenstein-Hawking theory, the temperature of a black hole is given by and the emitted radiation follows a blackbody distribution. For the Earth's mass, K, while for a solar mass, nK, both less than the temperature of the cosmic microwave . The Bekenstein-Hawking entropy formula for a black hole. For r0 > 0 the 3-brane carries some excess energy E above its extremal value, and the BH entropy is also non-vanishing. - TBH = - 1 87rcgH' (1.4 SBH = CA, (l-5) 1 S=,, were first derived quantum mechanically. English: The Bekenstein-Hawking entropy of a black hole is proportional to the surface area of the black hole as expressed in Planck units. conjectures in modern physics. conjectures in modern physics. The increase in the black hole entropy will compensate, and most frequently over-compensate, for the loss in the ordinary entropy outside it. Bob Walance said: Jacob Bekenstein asserts that the entropy of a black hole is proportional to its area rather than its volume. The proportionality between black hole entropy and area is derived from classical thermodynamics. Proposal : Geometric Entropy • in a theory of quantum gravity, for any sufficiently large region 738 J.D. For black holes on the other hand, the corresponding Bekenstein-Hawking' 2' 31 formulas --- -. 06.07.22 | Comment? PHYSICAL REVIEW D VOLUME 7, NUMBER 8 15 A PRI L 1973 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. Comments: 4 Pages. 16), 137, "An Alternative Approach to Black Hole Entropy." Bekenstein attributes the formulation of the equation (136, eq. Black holes and entropy Physical Review D. 7: 2333-2346. Black holes and entropy J. Bekenstein Published 15 April 1973 Physics Physical Review D There are a number of similarities between black-hole physics and thermodynamics. DOI: 10.1007/Bf02762768 : 1: 1973: Bekenstein JD.
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