Spacetime and Geometry

Spacetime and Geometry: An Introduction to General Relativityprovides a lucid and thoroughly modern introduction to general relativity for advanced undergraduates and graduate students. It introduces modern techniques and an accessible and lively writing style to what can often be a formal and intimidating subject. Readers are led from physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein’s equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology.

Table of Contents

CHAPTER 1 Special Relativity and Flat Spacetime

CHAPTER 2 Manifolds

CHAPTER 3 Curvature

CHAPTER 4 Gravitation

CHAPTER 5 The Schwarzschild Solut ion

CHAPTER 6 More General Black Ho les

CHAPTER 7 Perturbation Theory and Gravitatio nal Radiation

CHAPTER 8 Cosmo logy

CHAPTER 9 Quantum Field Theory in Curved Spacetime

APPENDIX A Maps between Manifolds

APPENDIX 8 Diffeomorphisms and Lie Derivatives

APPENDIX C Submanifolds

APPENDIX D Hypersurfaces

APPENDIX E Stokes’s Theorem

APPENDIX F Geodesic Congruences

APPENDIX G Conformal Transformations

APPENDIX H Conformal Diagrams

APPENDIX I The Parallel Propagator

APPENDIX J Noncoordinate Bases

About the Author

Sean Carroll is Homewood Professor of Natural Philosophy at Johns Hopkins University and Fractal Faculty at the Santa Fe Institute. His research focuses on fundamental issues in quantum mechanics, gravitation, statistical mechanics, and cosmology. He has wide-ranging interests, including in philosophy, complexity theory, and information.

Carroll is an active science communicator, and has been blogging regularly since 2004. His textbook “Spacetime and Geometry” has been adopted by a number of universities for their graduate courses in general relativity. He is a frequent public speaker, and has appeared on TV shows such as The Colbert Report and Through The Wormhole with Morgan Freeman. He has produced a set of lectures for The Teaching Company on dark matter and dark energy, and another on the nature of time. He has served as a science consultant for films such as Thor and TRON: Legacy, as well as for TV shows such as Fringe and Bones.

His 2010 popular book, “From Eternity to Here,” explained the arrow of time and connected it with the origin of our universe. “The Particle at the End of the Universe,” about the Large Hadron Collider and the quest to discover the Higgs boson, was released November 2012, “The Big Picture: On the Origins of Life, Meaning, and the Universe Itself” in May 2016, and “Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime” in 2019. His next book project is “The Biggest Ideas in the Universe,” which will consist of three books. The first, “Space, Time, and Motion,” appears in September 2022.