## An Introduction to Black Holes, Information and the String Theory Revolution: The Holographic UniverseOver the last decade the physics of black holes has been revolutionized by developments that grew out of Jacob Bekenstein's realization that black holes have entropy. Stephen Hawking raised profound issues concerning the loss of information in black hole evaporation and the consistency of quantum mechanics in a world with gravity. For two decades these questions puzzled theoretical physicists and eventually led to a revolution in the way we think about space, time, matter and information. This revolution has culminated in a remarkable principle called “The Holographic Principle”, which is now a major focus of attention in gravitational research, quantum field theory and elementary particle physics. Leonard Susskind, one of the co-inventors of the Holographic Principle as well as one of the founders of String theory, develops and explains these concepts. |

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### Contents

The Schwarzschild Black Hole | 3 |

Scalar Wave Equation in a Schwarzschild Background | 25 |

Quantum Fields in Rindler Space | 31 |

Entropy of the Free Quantum Field in Rindler Space | 43 |

Thermodynamics of Black Holes | 51 |

The Stretched Horizon | 61 |

The Laws of Nature | 69 |

The Puzzle of Information Conservation in Black Hole | 81 |

Horizons and the UVIR Connection | 95 |

Entropy Bounds | 101 |

The Holographic Principle and Anti de Sitter Space | 127 |

Black Holes in a Box | 141 |

Entropy of Strings and Black Holes | 165 |

179 | |

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### Common terms and phrases

AdS space baryon baryon number black hole complementarity boundary Chapter classical compute correlation cosmology cutoff D-branes defined degrees of freedom density matrix described dimensional dimensionless dimensions distant observer diverges eigenvalues entropy bound entropy density equation evaporation exponentially Fidos finite fluctuations form dr2 free string freely falling observer Frefos frequency gauge geometry given gravitational Hamiltonian Hawking radiation holographic bound Holographic Principle infalling observer infinite infinity interactions invariant let us consider light cone light rays light sheet light-like mass massless maximum entropy metric Minkowski space negative expansion number of degrees particle horizon Penrose diagram physics Planck length Planck units proton quantum field theory quantum mechanics quantum Xerox region Rindler energy Rindler space scalar field scale Schwarzschild black hole Schwarzschild radius shell shown in Figure singularity Sitter space space-like surfaces space-time spatial spherical stretched horizon string theory subsystem supersymmetry symmetry temperature thermal entropy thermodynamics transverse vacuum

### References to this book

Introduction to General Relativistic and Scalar-tensor Cosmologies Marcelo Samuel Berman Limited preview - 2007 |