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An Introduction to Gravity
出版済み 3-5週間でお届けいたします。
Author: Franklin, Joel (Reed College, Oregon) Publisher: Cambridge University Press ISBN: 9781009389709 Cover: HARDCOVER Date: 2024年04月 DESCRIPTION Einstein's theory of gravity can be difficult to introduce at the undergraduate level, or for self-study. One way to ease its introduction is to construct intermediate theories between the previous successful theory of gravity, Newton's, and our modern theory, Einstein's general relativity. This textbook bridges the gap by merging Newtonian gravity and special relativity (by analogy with electricity and magnetism), a process that both builds intuition about general relativity, and indicates why it has the form that it does. This approach is used to motivate the structure of the full theory, as a nonlinear field equation governing a second rank tensor with geometric interpretation, and to understand its predictions by comparing it with the, often qualitatively correct, predictions of intermediate theories between Newton's and Einstein's. Suitable for a one-semester course at junior or senior level, this student-friendly approach builds on familiar undergraduate physics to illuminate the structure of general relativity. Moves step-by-step through intermediate theories and introduces interesting predictions of GR early, motivating students to learn the mathematics needed to understand and solve the full field equations Uses multiple approaches to study the same physical effect, allowing students to appreciate results from easier methods before tackling the more challenging ones Introduces differential geometry in a simpler flat spacetime setting rather than a fully abstract introduction, to help students understand what is involved in developing a covariant divergence, Laplacian, etc A variety of 225 end-of-chapter exercises - with solutions for instructors - invite students to further explore the physical implications of GR Supported by a highly focused symbolic package for calculating differential geometric quantities, allowing students to concentrate on solving Einstein's equation, compare solutions in different coordinate systems, and consider modifications of general relativity TABLE OF CONTENTS 1. Newtonian gravity 2. Transformation and tensors 3. The Riemann tensor and Einstein's equation 4. Vacuum solutions and geodesics 5. Gravitational waves and radiation 6. Gravitational sources 7. Field theories and gravity Appendix A. Lorentz transformations and special relativity Appendix B. Runge-Kutta methods Appendix C. Curvature in D = 1, 2
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