By Leonard Susskind

Over the past decade the physics of black holes has been revolutionized via advancements that grew out of Jacob Bekenstein’s awareness that black holes have entropy. Steven Hawking raised profound concerns about 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 finally resulted in a revolution within the approach we expect approximately house, time, topic and data. This revolution has culminated in a impressive precept known as "The Holographic Principle", that is now an enormous concentration of consciousness in gravitational learn, quantum box concept and straightforward 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 options.

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The local geometry of a limiting black hole horizon is of course Rindler space. Let us consider the Rindler energy of the horizon. By deﬁnition it is conjugate to the Rindler time ω. 8) Here ER is the Rindler energy which is of course the eigenvalue of the Rindler Hamiltonian. We assume that for a large black hole the Rindler energy is a function of the mass of the black hole. 12) and The Rindler energy and the Schwarzschild mass are both just the energy of the black hole. The Schwarzschild mass is the energy as reckoned by observers at inﬁnity using t-clocks, while the Rindler energy is the (dimensionless) energy as deﬁned by observers near the horizon using ω-clocks.

9) are found to have smooth limits as → 0, as long as the points (X, Y, u) and (X , Y , u ) are kept away from the horizon. Therefore such quantities can be said to decouple from the degrees of freedom within a distance of the horizon. A much more singular quantity which will be of great concern in future lectures is the entropy of the vacuum state. 17 to obtain the entropy. 14 can be thought of as both entanglement and thermal entropy in the special case of the Rindler space density matrix. 30.

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. As we have seen, the relativistic analogue of a uniformly accelerated frame is Rindler space.