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Intended for graduate and advanced undergraduate students, this textbook is a thoroughly modern introduction to and a self-contained treatise on the theoretical and mathematical fundamentals of General Relativity. The chapters are organized into three parts, with the first covering Maxwell's theory of electromagnetism, the relativistic Kepler problem, and the systematics of the underlying geometry, with the more abstract notion of the fibre bundle relegated to the Appendix. The second part begins with a derivation of the Einstein equations and leads to topics such as cosmology, black holes, causal structures, and action principles. The third part covers the canonical formulation of field theory in general and General Relativity in particular, leading to the concept of the total energy in General Relativity and quantum phenomena with event horizons. The book minimizes historical references, focuses on modern tools, examples, and applications, and emphasizes the commonalities between relativistic gravity and gauge theory.
List of contents
Preface; Part I. Relativity and Geometry: 1. Electromagnetism and special relativity; 2. Particle motion under relativistic gravity; 3. Calculus on manifolds; 4. Riemannian geometry; 5. Maurer-Cartan; Part II. General Relativity: 6. The Einstein equation; 7. Cosmology in brief; 8. Spherically symmetric solutions; 9. Action principle and energy-momentum tensors; 10. More solutions; 11. Causal structures; Part III. Canonical Field Theories with Gravity: 12. An excursion: constrained dynamics; 13. Arnowitt-Deser-Misner; 14. Quantum fields and relativistic horizons; Appendix Fibre Bundles; List of illustrations; Index.
