Spacetime and Geometry An Introduction to General Relativity

Spacetime and Geometry is an introductory textbook on general relativity, specifically aimed at students. Using a lucid style, Carroll first covers the foundations of the theory and mathematical formalism, providing an approachable introduction to what can often be an intimidating subject. Three major applications of general relativity are then discussed: black holes, perturbation theory and gravitational waves, and cosmology. Students will learn the origin of how spacetime curves (the Einstein equation) and how matter moves through it (the geodesic equation). They will learn what black holes really are, how gravitational waves are generated and detected, and the modern view of the expansion of the universe. A brief introduction to quantum field theory in curved spacetime is also included. A student familiar with this book will be ready to tackle research-level problems in gravitational physics.

1. Special relativity and flat spacetime; 2. Manifolds; 3. Curvature; 4. Gravitation; 5. The Schwarzchild solution; 6. More general black holes; 7. Perturbation theory and gravitational radiation; 8. Cosmology; 9. Quantum field theory in curved spacetime; 10. Appendixes; Bibliography; Index.

Sean M. Carroll is Research Professor of Physics at the California Institute of Technology. His research focuses on general relativity, cosmology, field theory, statistical mechanics, and quantum mechanics. He is the recipient of numerous awards, including the Gemant Award from the American Institute of Physics, the Winton Science Book Prize from the Royal Society, a Guggenheim fellowship, and teaching awards from Massachusetts Institute of Technology and the University of Chicago.