## Table of Contents

**Table of Contents**

Preface

List of figures

Introduction

Part I: Hyperbolic Equationsâ€™ Theory

Chapter 1. Hyperbolic Equations

Chapter 2. Fundamental Solutions

Chapter 3. How to Build the Fundamental Solution

Part II: The Cauchy Problem in General Relativity

Chapter 4. Linear Systems of Normal Hyperbolic Form

Chapter 5. Linear System from a Non-linear Hyperbolic System

Chapter 6. General Relativity and the Causal structure of Space-

Time

Part III: A Modern Perspective

Chapter 7. Riemannâ€™s method in Gravitational Radiation Theory

Appendices

References

Index

**Keywords**: Mathematical Relativity, General Relativity, PDE, Pure Analysis, Black Hole, Black Hole Collisions, Physics, Mathematics, Mathematical Physics, Partial Differential Equations, Riemann Kernel, Hyperbolic Equations, Cauchy problem.

**Audience**: Math students, Physics Students, Mathematical Relativity Researchers and Professors, General Relativity Professors and students, Pure Analysis students and professors. Eventually, people who have interest in Mathematical Relativity, General Relativity, Partial differential equations and Pure Analysis.

**Reviews**

“This is an excellent book that can be used to introduce the reader to the theory of hyperbolic equations and to the mathematical theory of gravitational waves and Einstein equations. Several basic concepts such as wavelike propagation, fundamental solution, Riemann kernel and its existence, world function and its role in the fundamental solution, characteristic conoid, are well presented. The reader is then offered the opportunity to learn in detail how Choquet-Bruhat proved existence and uniqueness of the solution of vacuum Einstein equations with non-analytic Cauchy data. Last, an introduction to some important aspects of high-speed black hole collisions, a masterpiece work of D’Eath and Payne, is presented. The appendices on Sobolev spaces and Kasner spacetime are also very useful, as well as the suggested literature at the end. The author should be congratulated for having written a book of high pedagogical value for future generations of research workers in general relativity.” Giampiero Esposito, INFN Sezione di Napoli, Naples, Italy