By Leonard Susskind
During the last decade the physics of black holes has been revolutionized through 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 a global with gravity. for 2 many years those questions wondered theoretical physicists and at last resulted in a revolution within the approach we predict approximately house, time, subject and data. This revolution has culminated in a striking precept referred to as The Holographic precept , that's now an enormous concentration of awareness in gravitational examine, quantum box thought and common particle physics. Leonard Susskind, one of many co-inventors of the Holographic precept in addition to one of many founders of String thought, develops and explains those recommendations.
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Extra resources for An Introduction To Black Holes Information And The String Theory
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.
We see that the correct condition must be that at some small distance ρo , an eﬀective “membrane” is kept at a ﬁxed temperature T (ρo ) = 2π1ρo by an inﬁnite heat reservoir. It will prove useful later to G/c3 locate the membrane at a distance of order the Planck length P = where quantum gravitational or string eﬀects become important. Such a ﬁctitious membrane at Planckian distance from the horizon is called the stretched horizon. We will see later that the stretched horizon has many other physical properties besides temperature, although it is completely unseen by observers who fall freely through it.
Thus kX = 2nX π B where B is the size of the torus. 15) Entropy of the Free Quantum Field in Rindler Space 47 The entropy stored in the ﬁeld χk can be estimated from the entropy density of a 1+1 dimensional massless free boson at temperature 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.