Conformal Methods in General Relativity 1st Edition by Juan Valiente Kroon ISBN 1107033896 9781107033894

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Product details:

ISBN 10: 1107033896

ISBN 13: 978-1107033894

Author:  Juan A. Valiente Kroon 

Conformal Methods in General Relativity 1st Edition: This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein’s theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this the perfect reference companion on the topic.

 

Conformal Methods in General Relativity 1st Edition Table of contents:

• 1 – Introduction

Part I: Geometric Tools

• 2 – Differential Geometry
• 3 – Spacetime Spinors
• 4 – Space Spinors
• 5 – Conformal Geometry

Part II: General Relativity and Conformal Geometry

• 6 – Conformal Extensions of Exact Solutions
• 7 – Asymptotic Simplicity
• 8 – The Conformal Einstein Field Equations
• 9 – Matter Models
• 10 – Asymptotics

Part III: Methods of the Theory of Partial Differential Equations

• 11 – The Conformal Constraint Equations
• 12 – Methods of the Theory of Hyperbolic Differential Equations
• 13 – Hyperbolic Reductions
• 14 – Matter Models

Part IV: Applications

• 15 – De Sitter-Like Spacetimes
• 16 – Minkowski-Like Spacetimes
• 17 – Anti-de Sitter-Like Spacetimes
• 18 – Characteristic Problems for the Conformal Field Equations
• 19 – Static Solutions
• 20 – Spatial Infinity

 

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