A Student's Manual for A First Course in General Relativity

This comprehensive student manual has been designed to accompany the leading textbook by Bernard Schutz, A First Course in General Relativity, and uses detailed solutions, cross-referenced to several introductory and more advanced textbooks, to enable self-learners, undergraduates and postgraduates to master general relativity through problem solving. The perfect accompaniment to Schutz's textbook, this manual guides the reader step-by-step through over 200 exercises, with clear easy-to-follow derivations. It provides detailed solutions to almost half of Schutz's exercises, and includes 125 brand new supplementary problems that address the subtle points of each chapter. It includes a comprehensive index and collects useful mathematical results, such as transformation matrices and Christoffel symbols for commonly studied spacetimes, in an appendix. Supported by an online table categorising exercises, a Maple worksheet and an instructors' manual, this text provides an invaluable resource for all students and instructors using Schutz's textbook.

Preface; 1. Special relativity; 2. Vector analysis in special relativity; 3. Tensor analysis in special relativity; 4. Perfect fluids in special relativity; 5. Preface to curvature; 6. Curved manifolds; 7. Physics in curved spacetime; 8. The Einstein field equations; 9. Gravitational radiation; 10. Spherical solutions for stars; 11. Schwarzschild geometry and black holes; 12. Cosmology; Appendix A. Acronyms and definitions; Appendix B. Useful results; References; Index.