An Introduction to Black Holes, Information and the String Theory Revolution: The Holographic Universe

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OECD Publishing, Jan 1, 2005 - Science - 183 pages
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- A unique exposition of the foundations of the quantum theory of black holes including the impact of string theory, the idea of black hole complementarily and the holographic principle
bull; Aims to educate the physicist or student of physics who is not an expert on string theory, on the revolution that has grown out of black hole physics and string theory
  

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Page v - Jorgenson is a member of the National Academy of Sciences and the American Academy of Arts and Sciences.
Page 103 - A/4G. But now we can use the second law of thermodynamics to tell us that the original entropy inside F had to be less than or equal to A/4G. In other words the maximum entropy of a region of space is proportional to its area measured in Planck units. Such bounds are called holographic. 2.2. ENTROPY ON LIGHT-LIKE SURFACES We will see that it is most natural to define holographic entropy bounds on light-like surfaces [2] as opposed to space-like surfaces. Under certain circumstances the bounds can...
Page 102 - ... not really a property of a given system but also involves ones state of knowledge of the system. To define entropy we begin with some restrictions that express what we know, for example, the energy within certain limits, the angular momentum and whatever else we may know. The entropy is by definition the logarithm of the number of quantum states that satisfy the given restrictions. There is another concept that we will call the maximum entropy. This is a property of the system. It is the logarithm...
Page 103 - Suppose we have a thermodynamic system with entropy 5 that is completely contained within F. The total mass of this system can not exceed the mass of a black hole of area A or else it will be bigger than the region. Now imagine collapsing a spherically symmetric shell of matter with just the right amount of energy so that together with the original mass it forms a black hole which just fills the region. In other words the area of the horizon of the black hole is A. This is shown in figure (13). The...
Page 110 - The function a(t) is assumed to grow as a power of t. a(t) = a0f? (2.8) Lets also make the usual simplifying cosmological assumptions of homogeneity. In particular we assume that the spatial entropy density (per unit d volume) is homogeneous. Later, following Bousso, we will relax these assumptions. At time t we consider a spherical region F of volume V and area A. The boundary (d — l)-sphere, <9F, will play the same role as the screen in the previous discussion. The light-sheet is now defined...
Page 137 - The situation is the same as in matrix theory where we identify the N eigenvalues of the matrices in eq.(3.18) to be the coordinates zm of the N D3-branes. As in matrix theory the geometry is noncommutative and only configurations in which the six matrix valued fields commute have a classical interpretation. However the radial coordinate z = \/zmzm can be defined by A question which is often asked is; Where are the D3-branes located in the AdS space? The usual answer is that they are at the horizon...
Page 132 - Smax~-jp-p- (3.8) In other words when R/lp becomes large the holographic description requires a reduction in the number of independent degrees of freedom by a factor lp/R. To say it slightly differently, the holographic principle implies a complete description of all physics in the bulk of a very large AdS space in terms of only lp/R degrees of freedom per spatial Planck volume. 3.3. THE ADS/CFT CORRESPONDENCE The correspondence between string theory in AdS(5...
Page 137 - D3-branes which are nominally located at the origin of the coordinate z in eq. (3.3). The location of a point on a 3 brane is defined by six coordinates z,0)5.
Page 139 - ... the number of degrees of freedom needed to describe the region y > 6 [26]. The UV/IR connection implies that this region can be described in terms of an ultraviolet regulated theory with a cutoff length 6. Consider a patch of the boundary with unit coordinate area. Within that patch there are 1/J3 cutoff cells of size 6.
Page 134 - ... dimensionless parameters. These are: 1. The radius of curvature of the AdS space measured in string units R/ls 2. The dimensionless string coupling constant g. The string coupling constant and length scale are are related to the ten dimensional Planck length and Newton constant by l\ = ff2/s8 = G (3.10) On the other side of the correspondence, the gauge theory also has two constants.

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AN INTRODUCTION TO BLACK HOLES, INFORMATION AND THE STRING THEORY ...
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An Introduction to Black Holes, Information and the String Theory ...
An Introduction to Black Holes, Information and the String Theory Revolution: The Holographic Universe. Leonard Susskind and James Lindesay ...
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Open Questions: Black Holes
Leonard Susskind; James Lindesay – An Introduction to Black Holes, Information, and the String Theory Revolution: The Holographic Universe ...
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An introduction to Black Holes, Information and the String Theory ...
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Department of Physics and Astronomy
An Introduction to Black Holes, Information, and the String Theory Revolution, James Lindesay, CERN Courier, Oct. 2005. Scientific Eschatology. ...
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A 1 Prostor a jeho člověk / eds. Michal Ajvaz, Ivan M. Havel, Monika Mitášová Praha : Vesmír, 2004 39 723 JONÁŠ, Jiří a kol.: Nobelova cena za ekonomii ...
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About the author (2005)

Leonard Susskind is the Felix Bloch Professor in theoretical physics at Stanford University. He is the author of The Cosmic Landscape , The Black Hole War, and TheTheoretical Minimum: What You Need to Know to Start Doing Physics. Susskind is a member of the National Academy of Science and the American Academy of Arts and Sciences, and the recipient of numerous prizes including the science writing prize of the American Institute of Physics for his Scientific American article on black holes.

James Lindesay is a Professor of Physics at Howard University, and was the founding Director of the Computational Physics Lab. He has been a visiting professor at Hampton University and Stanford University and a visiting faculty scientist at the Massachusetts Institute of Technology.

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