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Table of contents
Part I. Fundamentals of General Relativity: Introduction, Canonical Formulation and Perturbation Theory
Chapter 1. Introduction
1.1. Gravitatio mundi, a brief historical prelude
1.2. The advent of relativity
1.3. Geometry, gravity and motion
1.4. Gravitational waves and extreme-mass-ratio inspirals
1.5. The self-force problem
Chapter 2. Canonical General Relativity
2.1. Introduction
2.2. Lagrangian formulation
2.3. Canonical formulation of general eld theories
2.4. Canonical formulation of general relativity
2.5. Applications
Chapter 3. General Relativistic Perturbation Theory
3.1. Introduction
3.2. General formulation of perturbation theory
3.3. Perturbations of the Schwarzschild-Droste spacetime
3.4. Perturbations of the Kerr spacetime
Part II. Novel Contributions: Entropy, Motion and Self-Force in General Relativity
Chapter 4. Entropy Theorems and the Two-Body Problem
4.1. Introduction
4.2. Entropy theorems in classical mechanics
4.3. Entropy theorems in general relativity
4.4. Entropy in the gravitational two-body problem
4.5. Conclusions
Chapter 5. The Motion of Localized Sources in General Relativity: Gravitational Self-Force from Quasilocal Conservation Laws
5.1. Introduction: the self-force problem via conservation laws
5.2. Setup: quasilocal conservation laws
5.3. General derivation of the gravitational self-force from quasilocal conservation laws
5.4. Application to the Gralla-Wald approach to the gravitational self-force
5.5. Discussion and conclusions
5.6. Appendix: conformal Killing vectors and the two-sphere
Chapter 6. A Frequency-Domain Implementation of the Particle-without-Particle Approach to EMRIs
6.1. Introduction
6.2. The scalar self-force
6.3. The Particle-without-Particle method
6.4. Frequency domain analysis
6.5. Numerical implementation and results
Chapter 7. Conclusions
