By Leonard Susskind

During the last decade the physics of black holes has been revolutionized by means of advancements that grew out of Jacob Bekenstein s consciousness that black holes have entropy. Stephen Hawking raised profound concerns in regards to the lack of details in black gap evaporation and the consistency of quantum mechanics in an international with gravity. for 2 many years those questions wondered theoretical physicists and finally ended in a revolution within the method we expect approximately area, time, subject and data. This revolution has culminated in a extraordinary precept known as The Holographic precept , that is now a tremendous concentration of realization in gravitational examine, quantum box thought and straightforward particle physics. Leonard Susskind, one of many co-inventors of the Holographic precept in addition to one of many founders of String concept, develops and explains those recommendations.

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The other wall of the box is provided by the repulsive potential V (u) = k 2 exp(2u) which becomes large when u > −log k. Thus we may approximate the potential by a second wall at u = u1 = −log k. 3) n where the mode (n, k) has frequency λ(n, k). 5) Thus far the quantization rules are quite conventional. 8) These particles constitute the thermal atmosphere. The reader might wonder what goes wrong if we choose the state which is annihilated by the a’s. Such a state is not at all invariant under translations of the original Minkowski coordinates Z and T .

16) where T is the temperature. 18, the integral must be cut oﬀ when k > 1 . This is because when k = 1 the potential is already large at u = uo so that the entire contribution of χk is supressed. 19 we see two important features of the entropy of Rindler space. The ﬁrst is that it is proportional to the transverse area of the horizon, B 2 . One might have expected it to diverge as the volume of space, but this is not the case. The entropy is stored in the vicinity of the stretched horizon and therefore grows only like the area.

13). Quantum mechanically we must expect this picture to break down by the time the infalling particle has been squeezed to within a Planck distance from the horizon. The Frefos of course see the matter behaving in a totally unexceptional way. Horizo n pρ ≈ pτ ≈ 2pZ expω = 2pZ exp( Fig. 13 Sedimentary layers of infalling matter on horizon 24 Black Holes, Information, and the String Theory Revolution Chapter 2 Scalar Wave Equation in a Schwarzschild Background In Chapters 3 and 4 we will be concerned with the behavior of quantum ﬁelds near horizons.