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# Topic: Black hole entropy

 Black hole - Wikipedia, the free encyclopedia Supermassive fl holes containing millions to billions of solar masses could also form wherever a large number of stars are packed in a relatively small region of space, or by large amounts of mass falling into a "seed" fl hole, or by repeated fusion of smaller fl holes. Black holes require the general relativistic concept of a curved spacetime: their most striking properties rely on a distortion of the geometry of the space surrounding them. The "surface" of a fl hole is the so-called event horizon, an imaginary surface surrounding the mass of the fl hole. en.wikipedia.org /wiki/Black_hole   (4692 words)

 Black hole entropy - Wikipedia, the free encyclopedia Black hole entropy is entropy carried by a fl hole. If fl hole carried no entropy, it would be possible to violate the second law of thermodynamics by throwing mass into the fl hole. The fact that the fl 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. en.wikipedia.org /wiki/Black_hole_entropy   (333 words)

 5 Calculations of Black Hole Entropy Another approach to the calculation of fl hole entropy has been to attribute it to the ``entanglement entropy'' resulting from quantum field correlations between the exterior and interior of the fl hole [24, 31, 57]. In common with the entanglement entropy and thermal atmosphere approaches, fl hole entropy is explained as arising from the quantum field degrees of freedom outside the fl hole. Since the formula for entropy has a nontrivial functional dependence on energy and charges, it is hard to imagine that the agreement between the ordinary entropy of the weak coupling states and fl hole entropy could be the result of a random coincidence. relativity.livingreviews.org /Articles/lrr-2001-6/node7.html   (2339 words)

 Black Hole Information Loss What we start with is a pure state and a fl hole of mass M. What we end up with is a thermal state and a fl hole of mass M. We have found a process (apparently) which converts a pure state into a thermal state. Perhaps the fl hole is not the same after it has evaporated to mass M as it was initially at mass M. Or perhaps there is some subtle correlation in the Hawking radiation that we are missing, but that supplies the missing information about the pure state. This is a profound result, since the thermodynamical entropy is obtained at a semiclassical level (in fact, due to some quirks which I suspect are related to the non-linearity of gravity, it is essentially classical). www.xs4all.nl /~johanw/PhysFAQ/Relativity/BlackHoles/info_loss.html   (882 words)

 Problems in black-hole entropy interpretation   (Site not responding. Last check: 2007-10-21) Calculations on entanglement entropy were performed by various authors in a wide class of situations, in flat spaces as in curved ones [9-11]. Nevertheless, it is possible to understand the extremal case as a particular case of fl hole without requiring a limitation of fl-hole thermodynamics laws [29]. We conjecture that this relation of the gravitational entropy with boundary structure of the space-time is in a certain sense a hint towards an interpretation based on dynamical degrees of freedom associated to the vacuum states in non-trivial topologies. www.sif.it /cimento/tocb/112.02-03/26/26.html   (5500 words)

 Physical Laws Collide in a Black Hole Bet Black holes provide a rare theoretical arena where quantum mechanics and general relativity come together, recreating the extreme conditions thought to have existed in the earliest moments of the big bang. Black holes are apparently an inevitable consequence of the laws describing gravity and how it shapes space and time. But from the point of view of an observer outside the fl hole, all this history -- past, present, and future -- would be simultaneously displayed in two dimensions on the horizon. www.theory.caltech.edu /people/preskill/blackhole_bet.html   (2206 words)

 Citebase - Black hole entropy: statistical mechanics agrees thermodynamics It is demonstrated on the two-dimensional example that the (quantum) thermodynamical entropy of a hole coincides (including UV-finite terms) with its statistical-mechanical entropy calculated according to 't Hooft and regularized by Pauli-Villars. Entropy of the Kerr-Newman fl hole is calculated via the brick wall method with maintaining careful attention to the contribution of superradiant scalar modes. In this paper the entropy of an eternal Schwarzschild fl hole is studied in the limit of infinite fl hole mass. citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:hep-th/9601154   (1018 words)

 Citebase - Hawking radiation without black hole entropy On the other hand, the classical laws of fl hole mechanics are intrinsically linked to the Einstein equations of general relativity (or their perturbative extension into either semiclassical quantum gravity or string-inspired scenarios). In particular, the laws of fl hole thermodynamics, and the identification of the entropy of a fl hole with its area, are inextricably linked with the dynamical equations satisfied by the Lorentzian geometry: entropy is proportional to area (plus corrections) if and only if the dynamical equations are the Einstein equations (plus corrections). The sonic analog of a gravitational fl hole in dilute-gas Bose-Einstein condensates is investigated. citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:gr-qc/9712016   (1582 words)

 string theory on black hole entropy - Physics Help and Math Help - Physics Forums The calculation assumes that the\nandgt; fl hole interior can be neglected and the entropy comes from a new kind\nandgt; of dynamics attached to the surface area - there is no justification of\nandgt; this assumption. The entropy is not computed from string theory,\nbut from ``a simple but mysterious duality-invariant extension of\npreviously derived formulae for the number of D-brane states in string\ntheory.\'\' In the second paper, the authors state explicitly, very early\non, ``We have not been able to obtain a stringy derivation of the full\nexpression. But the trouble is\nthat for each new fl hole, the density of states and the horizon area\ndepend on a new set of charges, and have to be recalculated from scratch.\n\nIf you give me a brand new near-extremal fl hole, I would certainly\nexpect to get the right agreement again. www.physicsforums.com /showthread.php?threadid=43967   (7065 words)

 Re: black hole entropy & entanglement People believe that: 1) the entropy of a fl hole is proportional to the area of its event horizon and 2) if you squash too much stuff together, it forms a fl hole. Raphael's covariant version of the entropy bound is to say that the entropy contained in a null hypersurface which has the closed surface B as its boundary is less than A(B)/4, as long as the hypersurface is defined as being generated by null rays moving in the direction of decreasing area of the surface. Let me quote him on this to be precise: (hep-th/9905177) Covariant Entropy Conjecture (Bousso): Let M be a 4-dimensional spacetime on which Einstein's equation is satisfied with the dominant energy condition holding for matter. www.lns.cornell.edu /spr/1999-08/msg0017478.html   (459 words)

 Black Hole Entropy and Induced Gravity   (Site not responding. Last check: 2007-10-21) arises at tree-level while the entropy of quantum excitations is a one-loop quantity. is the surface area of the fl hole. We discuss the role of non-minimal coupling, relation Q to the Noether charges, and degrees of freedom that are responsible for the fl hole entropy in induced gravity [4,5]. www.physik.uni-leipzig.de /~bordag/FrolovAbstract   (214 words)

 1997 Banff Black Hole Conference Welcome to "Black Holes: Theory and Mathematical Aspects" conference homepage. We hope to cover such subjects as fl hole formation and scaling laws, fl hole collisions and numerical relativity, fl hole evaporation, entropy, and information, fl holes in non-Euclidean gravity and string theory, and fl holes and Planck-scale physics. Black Hole Conference Secretary, Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, Canada T6G 2J1 Phone: 1(403)492-8486 Fax: 1(403)492-0714 E-mail: grimard@phys.ualberta.ca www.phys.ualberta.ca /~frolov/blackhole/banff.html   (398 words)

 Black Hole Entropy in Quantum Gravity - Physics Help and Math Help - Physics Forums These are exotic objects which unlike the fl holes one sees evidence of in nature are electrically charged to the max. Quantum geometry is directly counting fluctuations of the event horizon, while string theory extrapolates the fl hole to weak coupling and counts states of strings (and branes) in flat spacetime. On the other hand, the problem is far more serious in the case of LQG because right out of the box there's an ambiguity in the fl hole entropy formula it produces and no apparent additional or unexplored structure in LQG from which a resolution might spring. www.physicsforums.com /showthread.php?t=6638   (1336 words)

 week111 More precisely, using quantum field theory on curved spacetime, he showed that a fl hole should radiate photons thermally, with a temperature T proportional to the surface gravity K at the event horizon. In other words, we hope that specifying the area A of the fl hole horizon specifies the macrostate, and that there are about N = exp(A/4) microstates corresponding to this macrostate. I presume you see what I'm leading up to: the idea of computing fl hole entropy using spin networks, which are designed precisely to describe "quantum geometries", as sketched in "week55", "week99", and "week110". math.ucr.edu /home/baez/week111.html   (1769 words)

 Renormalization of Black Hole Entropy (ResearchIndex)   (Site not responding. Last check: 2007-10-21) Abstract: INTRODUCTION One of the mysterious and challenging phenomena in general relativity is fl hole physics. Black holes formed from the gravitational collapse of massive stars are characterized by mass M, angular momentum J and charge Q, regardless of the process of their formation. Classically a fl hole prevents any particle from crossing its event horizon from the interior, and all the particles falling into it eventually run into the singularity. citeseer.ist.psu.edu /72398.html   (187 words)

 Time Travel Portal :: View topic - Black hole entropy reveals a 12th "dimension" The Beckenstein-Hawking fl hole entropy in string theory and its extensions, as expressed in terms of charges that correspond to central extensions of the supersymmetry algebra, has more symmetries than U-duality. It is suggested that the idea of spacetime is broader than usual, and that a larger "spacetime" is partially present in fl holes. Black hole entropy reveals a 12th "dimension" by Itzhak Bars. timetravelportal.com /viewtopic.php?t=615   (253 words)

 Learn more about Timeline of black hole physics in the online encyclopedia.   (Site not responding. Last check: 2007-10-21) Learn more about Timeline of fl hole physics in the online encyclopedia. 1972 - James Bardeen, Brandon Carter, and Stephen Hawking propose four laws of fl hole mechanics in analogy with the laws of thermodynamics, 2002 - Astronomers present evidence for the hypothesis that Sagittarius A* is a supermassive fl hole at the centre of the Milky Way galaxy, www.onlineencyclopedia.org /t/ti/timeline_of_black_hole_physics.html   (693 words)

 Collection of E-prints of Interest   (Site not responding. Last check: 2007-10-21) Black Holes: Scatterers, Absorbers and Emitters of Particles (hep-th/0106222) Entropy of massive fields near a fl hole and vacuum polarization: thermodynamics without statistical mechanics (gr-qc/0101055) Black hole entropy and the semiclassical approximation (hep-th/9404135) www.ictp.trieste.it /~shanki/pap-list-public/eprints.html   (1318 words)

 Black Hole References Macroscopic aspects of Calabi-Yau fl hole entropy in type II low energy effective field theory (outline and references). describe the brane interpretation of the entropy of axion free Calabi-Yau fl holes in M-theory/type II string theory. G.Horowitz, The origin of fl hole entropy in string theory, gr-qc/960404051 www.th.physik.uni-bonn.de /th/People/netah/papers/bhs/bh-lit.html   (421 words)

 Quantum Gravity and Black Hole Entropy   (Site not responding. Last check: 2007-10-21) In this approach, the quantum geometry of the region outside the fl hole is described using spin networks, while the quantum geometry of the horizon itself is described by a U(1) Chern-Simons theory. Counting the surface degrees of freedom for a horizon of fixed area, one can show that the entropy of a large non-rotating fl hole is proportional to its horizon area. Quantum Geometry of Isolated Horizons and Black Hole Entropy by Abhay Ashtekar, John Baez and Kirill Krasnov math.ucr.edu /home/baez/black   (175 words)

 Black Hole Entropy (ResearchIndex)   (Site not responding. Last check: 2007-10-21) And each larva, as it approaches the chrysalis stage and feels compelled to rise to the... 0.2: Temperatures of Extremal Black Holes - Amit Ghosh 0.2: Black Hole Entropy: Departures From Area Law - Mitra Saha (1995) citeseer.ist.psu.edu /32577.html   (215 words)

 DC MetaData for: Quantum Geometry and Black Hole Entropy   (Site not responding. Last check: 2007-10-21) Abstract: A `fl hole sector' of non-perturbative canonical quantum gravity is The quantum fl hole degrees of freedom are shown to be that the entropy of a large non-rotating fl hole is proportional to www.esi.ac.at /Preprint-shadows/esi510.html   (103 words)

 Black Holes The answer to this question is the shocking and amazing object known as the fl hole. Quantum mechanics turns fl holes from cold, eternal objects into hot shrinking thermodynamics. Thanks to the string duality revolution of the early nineties, a microscopic derivation for fl hole entropy has been discovered, at least in theory. superstringtheory.com /blackh   (124 words)

 Abhay Ashtekar : Recent Publications Ashtekar and K. Krasnov, Quantum Geometry and Black Holes, In: Black Holes, Gravitational Radiation and the Universe, edited by B. Iyer and B. Bhawal (Kluwer Dodrecht, 1999), p. Ashtekar, J. Baez and K. Krasnov, Quantum Geometry of Isolated Horizons and Black Hole Entropy, Advances in Theoretical and Mathematical Physics, 4, 1-95 (2000), gr-qc/0005126. Ashtekar, Quantum Geometry in Action: Big Bang and Black Holes, In: Graphs and Patterns in Mathematical and Theoretical Physics, Volume in honor of Dennis Sullivan (American Mathematical Society, 2003). gravity.psu.edu /people/Ashtekar/publications.html   (1856 words)

 Re: black hole entropy & entanglement   (Site not responding. Last check: 2007-10-21) If there is a certain >mass-energy per particle, then, it seems that the amount of information >N particles can carry grows faster than the classical case O(N) >but slower than the quantum case O(2^n). Regarding the fl hole, I suppose the answer is that we no longer have N particles after they go into the hole, so the formula above does not apply. If we leap ahead to the time when the entropy comes out again as Hawking radiation, the number of photons per unit mass will be inversely proportional to the temperature of the hole, which in turn will be inversely proportional to the mass. www.lns.cornell.edu /spr/1999-08/msg0017454.html   (289 words)

 Black Hole Entropy as derived by Stephen Hawking - EquationSheet Black Hole Entropy as derived by Stephen Hawking - EquationSheet Black Hole Entropy as derived by Stephen Hawking Pasting the above "text" into MathType 5.0 will enter the above equation and make it possible to edit, save, and use in applications such as MS Word. www.equationsheet.com /eqninfo/Equation-176.html   (54 words)

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