## Quantum Field Theory in Curved Spacetime and Black Hole ThermodynamicsIn this book, Robert Wald provides a coherent, pedagogical introduction to the formulation of quantum field theory in curved spacetime. He begins with a treatment of the ordinary one-dimensional quantum harmonic oscillator, progresses through the construction of quantum field theory in flat spacetime to possible constructions of quantum field theory in curved spacetime, and, ultimately, to an algebraic formulation of the theory. In his presentation, Wald disentangles essential features of the theory from inessential ones (such as a particle interpretation) and clarifies relationships between various approaches to the formulation of the theory. He also provides a comprehensive, up-to-date account of the Unruh effect, the Hawking effect, and some of its ramifications. In particular, the subject of black hole thermodynamics, which remains an active area of research, is treated in depth. This book will be accessible to students and researchers who have had introductory courses in general relativity and quantum field theory, and will be of interest to scientists in general relativity and related fields. |

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### Contents

Introduction and Overview | 2 |

12 Classical Black Hole Thermodynamics | 7 |

13 The Hawking Effect and its Ramifications | 9 |

Quantum Mechanical Preliminaries | 11 |

22 Quantum Mechanics | 18 |

23 Harmonic Oscillators | 22 |

Quantum Fields in Flat Spacetime | 32 |

32 Reformulation | 36 |

The Unruh Effect | 106 |

51 The Unruh Effect in Flat Spacetime | 107 |

52 Killing Horizons | 119 |

53 The Unruh Effect in Curved Spacetime | 124 |

Classical Black Hole Thermodynamics | 134 |

62 The Laws of Black Hole Mechanics | 140 |

The Hawking Effect | 152 |

71 Particle Creation by Black Holes | 153 |

33 Particle Interpretation | 47 |

Quantum Fields in Curved Spacetime | 54 |

41 Curved Spacetimes Global Hyperbolicity | 55 |

42 Construction of Quantum Field Theory in a Curved Spacetime | 58 |

43 Quantum Field Theory in Stationary Spacetimes | 62 |

44 Unitary Equivalence the Smatrix | 67 |

45 The Algebraic Approach | 74 |

46 The StressEnergy Tensor | 86 |

47 Other Linear Fields | 101 |

72 The Generalized Second Law | 164 |

73 Evaporation of Black Holes and Loss of Quantum Coherence | 176 |

Some Basic Definitions and Constructions Pertaining to Hilbert Spaces | 189 |

A2 Some Basic Constructions | 191 |

A3 Index Notation | 193 |

196 | |

202 | |

204 | |

### Other editions - View all

Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics Robert M. Wald No preview available - 1994 |

Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics Robert M. Wald No preview available - 1994 |

Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics Robert M. Wald No preview available - 1994 |

### Common terms and phrases

algebraic approach analogous asymptotic back-reaction bifurcate Killing horizon Cauchy surface choice classical corresponding curved spacetime defined denotes density matrix derivation dimensional discussion dynamical energy entropy evaporation event horizon exists extended Schwarzschild spacetime field theory constructions finite flat spacetime Fock space follows geodesic given globally hyperbolic globally hyperbolic spacetime gravity Hamiltonian harmonic oscillators Hawking effect Hilbert space inertial infinity initial data inner product isometries Killing field Killing horizon Klein-Gordon equation Klein-Gordon field laws of black linear map mathematical metric Minkowski spacetime Minkowski vacuum Note notion of particles null obtain operator ordinary particle creation particle interpretation prescription propagate properties quantum field theory quantum mechanical quantum theory region restriction S-matrix satisfying eq section 4.3 semiclassical solutions spacetime of fig stationary black hole stationary spacetime stress-energy tensor structure subspace symplectic temperature theorem theory in curved timelike tion uniquely unitarily inequivalent unitary equivalence Unruh effect vector space Weyl algebra

### Popular passages

Page 1 - Of greatest interest for the development of the analogy between the laws of black hole physics and the laws of thermodynamics...