Spacetime and Geometry: An Introduction to General Relativity PDF Download Ebook. Sean Carroll provides a lucid and thoroughly modern introduction to general relativity. With an accessible and lively writing style, it introduces modern techniques to what can often be a formal and intimidating subject.
Readers are led from the 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. For advanced undergraduates and graduate students, or anyone interested in astronomy, cosmology, physics, or general relativity.
This book’s purpose is more to review the basics and and introduce some notation, rather than to provide a self-contained introduction. Beyond that, some exposure to electromagnetism, Lagrangian mechanics, and linear algebra might be useful, but the essentials are included here.
The structure of the book should be clear. The first chapter is a review of special relativity and basic tensor algebra, including a brief discussion of classical field theory. The next two chapters introduce manifolds and curvature in some detail; some motivational physics is included, but building a mathematical framework is the primary goal. General relativity proper is introduced in Chapter Four, along with some discussion of alternative theories.
The next four chapters discuss the three major applications of GR: black holes (two chapters), perturbation theory and gravitational waves, and cosmology. Each of these subjects has witnessed an explosion of research in recent years, so the discussions here will be necessarily introductory, but I have tried to emphasize issues of relevance to current work. These three applications can be covered in any order, although there are interdependencies highlighted in the text. Discussions of experimental tests are sprinkled through these chapters.
Chapter Nine is a brief introduction to quantum field theory in curved spacetime; this is not a necessary part of a first look at GR, but has become increasingly important to work in quantum gravity and cosmology, and therefore deserves some mention. On the other hand, a few topics are scandalously neglected; the initial value problem and cosmological perturbation theory come to mind, but there are others. Fortunately there is no shortage of other resources.
The appendices serve various purposes: there are discussions of technical points which were avoided in the body of the book, crucial concepts which could have been put in various different places, and extra topics which are useful but outside the main development.
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