By Leonard Susskind

During the last decade the physics of black holes has been revolutionized through advancements that grew out of Jacob Bekenstein's awareness that black holes have entropy. Steven Hawking raised profound concerns in regards to the lack of info in black gap evaporation and the consistency of quantum mechanics in an international with gravity. for 2 a long time those questions questioned theoretical physicists and at last ended in a revolution within the manner we predict approximately area, time, topic and data. This revolution has culminated in a extraordinary precept referred to as "The Holographic Principle", that's now an immense concentration of recognition in gravitational examine, quantum box thought and easy 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 innovations.

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**Example text**

34) Thus, to the Fido near r = 2M G, the Schwarzschild clock appears to run at a very rapid rate. 17. The spatial location of the Fidos can be labeled by the angular coordinates (θ, φ) and any one of the radial variables r, r∗ , or ρ. Classically the Fidos can be thought of as mathematical ﬁctions or real but arbitrarily light 22 Black Holes, Information, and the String Theory Revolution systems suspended by arbitrarily light threads from some sort of suspension system built around the black hole at a great distance.

7, that is it coincides with the future horizon of the ﬁnal black hole geometry and is therefore found at r = 2M G. On the other hand, the horizon also extends into the Region A where the metric is just that of ﬂat space-time. In this region the value of r on the horizon grows from an initial value r = 0 to the value r = 2M G at the shell. 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.

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 ) . 27) In other words, the path integral deﬁning Ψ is computed as a transition matrix element between initial state χR and ﬁnal state χL . The inﬁnitesimal generator which pushes θ surfaces forward is just the Rindler Hamiltonian. Now we are prepared to compute the density matrix ρR . 30) This remarkable result, discovered by William Unruh in 1976 , says that the Fidos see the vacuum as a thermal ensemble with a density matrix of the Maxwell–Boltzmann type.