By Leonard Susskind

ISBN-10: 9812560831

ISBN-13: 9789812560834

ISBN-10: 9812561315

ISBN-13: 9789812561312

Over the past decade the physics of black holes has been revolutionized by means of advancements that grew out of Jacob Bekenstein s recognition that black holes have entropy. Stephen Hawking raised profound matters about the lack of details in black gap evaporation and the consistency of quantum mechanics in a global with gravity. for 2 a long time those questions questioned theoretical physicists and at last ended in a revolution within the means we predict approximately area, time, subject and knowledge. This revolution has culminated in a outstanding precept referred to as The Holographic precept , that is now an immense concentration of recognition in gravitational examine, quantum box conception and basic particle physics. Leonard Susskind, one of many co-inventors of the Holographic precept in addition to one of many founders of String idea, develops and explains those innovations.

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**Extra resources for An introduction to black holes, information and the string theory revolution : the holographic universe**

**Example text**

A small fraction of the particles carry very low angular momenta. For these particles, the walls are semi-transparent and the cavity slowly radiates its energy. This is the process ﬁrst discovered by Hawking and is referred to as Hawking radiation. The above description of Hawking radiation does not depend in any essential way on the free ﬁeld approximation. Indeed it only makes sense if there are interactions of suﬃcient strength to keep the system in equilibrium during the course of the evaporation.

It is evident from this discussion that the horizon is a global and not a local concept. In the Region A no local quantity will distinguish the presence of the horizon whose occurence is due entirely to the future collapse of the shell. Consider next a distant observer located on a trajectory with r >> 2M G. 11. The distant observer collects information that arrives at any instant from his backward light cone. Evidently such an observer never actually sees events on the The Schwarzschild Black Hole 19 areas Match here of 2-sp B’ A r < t= G M H r 2M =2 8 r=0 + G r=0 - Fig.

11) The eigenvalues ρj can be considered to be probabilities that the system is in the j th state. However, unlike the case of a coherent superposition of states, the relative phases between the states |j are random. There is one special case when the density matrix is indistinguishable from a pure state. This is the case in which only one eigenvalue ρj is Quantum Fields in Rindler Space 35 nonzero. 12) A quantitative measure of the departure from a pure state is provided by the Von Neumann entropy S = −T r ρ log ρ = − j ρj log ρj .

### An introduction to black holes, information and the string theory revolution : the holographic universe by Leonard Susskind

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