Description
CAMBRIDGE General Relativity A Geometric Approach 2017 Edition by Malcolm Ludvigsen
Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear and concise introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. All physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas are illustrated with worked examples. Solutions and hints to selected problems are provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity. Table of contents :- Part I. The Concept of Spacetime: 1. Introduction; 2. Events; Part II. Flat Spacetime and Special Relativity: 3. Flat spacetime; 4. The geometry of flat spacetime; 5. Energy; 6. Tensors; 7. Tensor fields; 8. Field equations; Part III. Curved Spacetime and Gravity: 9. Curved spacetime; 10. Curvature and gravity; 11. Null congruences; 12. Asymptotic flatness and symmetries; 13. Schwarzschild; 14. Black holes and singularities; Part IV. Cosmology: 15. The spacetime of the universe; 16. Relativistic cosmology; Solutions and hints to selected exercises; Bibliography; Index.