By Leonard Susskind

Over the past decade the physics of black holes has been revolutionized through advancements that grew out of Jacob Bekenstein s awareness 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 finally resulted in a revolution within the manner we expect approximately house, time, topic and data. This revolution has culminated in a impressive precept known as The Holographic precept , that is now a massive concentration of cognizance in gravitational examine, quantum box conception and effortless 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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Since in this region the ﬁeld χ(u) behaves like a free massless ﬁeld, the boundary condition would be expected to be that the ﬁeld is in the usual quantum ground state. In the next section we will see that this is not so. − 30 Black Holes, Information, and the String Theory Revolution Chapter 3 Quantum Fields in Rindler Space According to Einstein, the study of a phenomenon in a gravitational ﬁeld is best preceeded by a study of the same phenomenon in an accelerated coordinate system. In that way we can use the special relativistic laws of nature to understand the eﬀect of a gravitational ﬁeld.

21) To proceed further we must use the fact that Ψ(χL , χR ) is the ground state of the Minkowski Hamiltonian. General path integral methods may be brought to bare on the computation of the ground state wave functional. 22) The so-called Euclidean ﬁeld theory is deﬁned by replacing the time coordinate T by i X 0 . 24) Now a standard method of computing the ground state by path integration is to use the Feynman–Hellman theorem. Suppose we wish to compute Ψ(χL , χR ). 25) where the path integral is over all χ(x) with X 0 > 0 and Z is an appropriate normalization factor .

The simpest model for black hole formation involves a collapsing thin spherical shell of massless matter. For example, a shell of photons, gravitons, or massless neutrinos with very small radial extension and total energy M provides an example. To construct the geometry, we begin with the empty space Penrose diagram with the infalling shell represented by an incoming light-like line 16 Black Holes, Information, and the String Theory Revolution t=+ 8 Future Singularity + I III r = 8 H+ II H - t=- 8 IV Past Singularity r 2 t=+ 8 Future Singularity II H or iz on r = r r 1= + t=2 t=0 r= t=-1 = t -2 III 8 t=1 on iz or H - t=- 8 IV Past Singularity Penrose diagram for Schwarzschild black hole, showing regions (top) and curves of ﬁxed radial position and constant time (bottom) Fig.