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.

Table of Contents

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