By Leonard Susskind

During the last decade the physics of black holes has been revolutionized by way of advancements that grew out of Jacob Bekenstein s awareness that black holes have entropy. Stephen Hawking raised profound concerns about the lack of info 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 resulted in a revolution within the manner we expect approximately house, time, subject and data. This revolution has culminated in a impressive precept known as The Holographic precept , that is now an incredible concentration of awareness in gravitational examine, quantum box concept and common 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 suggestions.

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**Sample text**

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. Chapter 4 Entropy of the Free Quantum Field in Rindler Space In the real world, a wide variety of diﬀerent phenomena take place at diﬀerent temperature scales. At the lowest temperatures where only massless quanta are produced by thermal ﬂuctuations, one expects to ﬁnd a very weakly interacting gas of gravitons, photons, and neutrinos.

3 Horizon ρ=0 χR θ=0 Z Euclidean analogue of Rindler space for path integration The strategy for computing the path integral is to integrate over the ﬁelds in the ﬁrst wedge between θ = 0 and θ = δθ. The process can be iterated until the entire region X 0 > 0 has been covered. The integral over the ﬁrst wedge is deﬁned by constaining the ﬁelds at θ = 0 and θ = δθ. This deﬁnes a transfer matrix G in the Hilbert space of the ﬁeld conﬁguration χR . The matrix is recognized to be G = (1 − δθ HR ) .

As the particle freely falls past the horizon, the components pZ and pT may be regarded as constant or slowly varying. They are the components seen by Frefos. 37) 4M G Thus we ﬁnd the momentum of an infalling particle as seen by a Fido grows exponentially with time! 38) ρ(t) ≈ ρ(0)exp(− 4M G Locally the relation between the coordinates of the Frefos and Fidos is a time dependent boost along the radial direction. The hyperbolic boost angle is the dimensionless time ω. Eventually, during the lifetime of the black hole this boost becomes so large that the momentum of an infalling particle (as seen by a Fido) quickly exceeds the entire mass of the universe.