Clarity, readability, and rigor combine in the third edition of this widely used textbook to provide the first step into general relativity for advanced undergraduates with a minimal background in mathematics. Topics within relativity that fascinate astrophysics researchers and students alike are covered with Schutz's characteristic ease and authority, from black holes to relativistic objects, from pulsars to the study of the Universe as a whole. This third edition contains discoveries by astronomers that require general relativity for their explanation; two chapters on gravitational waves, including direct detections of gravitational waves and their observations' impact on cosmological measurements; new information on black holes and neutron stars; and greater insight into the expansion of the Universe. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, while the informal writing style and worked examples make the subject matter easily accessible.

Table of Contents

1 Special relativity

2 Vector analysis in special relativity

3 Tensor analysis in s pecial relativity

4 Perfect fluids in s pecial relat ivity

5 Preface to curvature

6 Curved manifolds

7 Physics in a curved s pacetime

8 The Einstein field equations

9 Fundamentals of gravitational radiation

10 Spherical solutions for stars

11 Schwarzschild geometry and black holes

12 Gravitational wave astronomy

13 Cosmology

About the Author

Bernard Schutz is a Professor in the School of Physics and Astronomy at Cardiff University, Wales, and Director (ret.) at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Germany. In 2019 he was elected a member of the US National Academy of Sciences, and in 2021, he was elected a fellow of the Royal Society, in recognition of his seminal contributions to relativistic astrophysics.