Table of Contents
List of figures
Part I: Hyperbolic Equations’ 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-
Part III: A Modern Perspective
Chapter 7. Riemann’s method in Gravitational Radiation Theory
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.
“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