Geometric Analysis of Hyperbolic Differential Equations: An Introduction

Its self-contained presentation and 'do-it-yourself' approach makes this the perfect guide for graduate students wishing to access recent literature in the field of mathematical relativity. It introduces all of the key tools and concepts from Lorentzian geometry and provides complete elementary proofs. No previous knowledge of geometry is required.

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Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required.