Asymptotic Analysis in General Relativity

by Daudé, Thierry

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Full title :Asymptotic Analysis in General Relativity.

Summary

Cover -- Series information -- Title page -- Copyright information -- Table of contents -- 1 Introduction to Modern Methods for Classical and Quantum Fields in General Relativity -- 1.1 Geometry of Black Hole Spacetimes -- 1.2 Quantum Field Theory on Curved Spacetimes -- 1.3 Conformal Geometry and Conformal Tractor Calculus -- 1.4 A Minicourse in Microlocal Analysis and Wave Propagation -- References -- 2 Geometry of Black Hole Spacetimes -- 2.1 Introduction -- 2.2 Background -- 2.2.1 Minkowski Space -- 2.2.2 Lorentzian Geometry and Causality -- 2.2.3 Conventions and Notation -- 2.2.4 Einstein Equation -- 2.2.5 The Cauchy Problem -- 2.2.6 Remarks -- 2.2.6.1 Bianchi Identities as a Hyperbolic System -- 2.2.6.2 Null Condition -- 2.2.6.3 Gauge Source Functions -- 2.2.6.4 Asymptotically Flat Data -- 2.2.6.5 Killing Initial Data -- 2.2.6.6 Komar Integrals -- 2.3 Black Holes -- 2.3.1 The Schwarzschild Solution -- 2.3.1.1 Gravitational Redshift -- 2.3.1.2 Orbiting Null Geodesics -- 2.3.2 Raychaudhouri Equation and Comparison Theory -- 2.3.3 The Apparent Horizon -- 2.3.4 Results on MOTS and the Trapped Region -- 2.3.5 Formation of Black Holes -- 2.3.6 Black Hole Stability -- 2.3.7 The Kerr Metric -- 2.4 Spin Geometry -- 2.4.1 Spinors on Minkowski Space -- 2.4.2 Spinors on Spacetime -- 2.4.3 Fundamental Operators -- 2.4.4 Massless Spin-s Fields -- 2.4.5 Killing Spinors -- 2.4.6 Algebraically Special Spacetimes -- 2.4.6.1 Petrov Type D -- 2.4.7 Spacetimes Admitting a Killing Spinor -- 2.4.8 GHP Formalism -- 2.5 The Kerr Spacetime -- 2.5.1 Characterizations of Kerr -- 2.6 Monotonicity and Dispersion -- 2.6.1 Monotonicity for Null Geodesics -- 2.6.2 Dispersive Estimates for Fields -- 2.7 Symmetry Operators -- 2.7.1 Symmetry Operators for the Kerr Wave Equation -- 2.7.2 Symmetry Operators for the Maxwell Field -- 2.8 Conservation Laws for the Teukolsky System.

This book provides a panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity.