Classical Mechanics and Relativity (2版)

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【簡介】 The text covers the entire domain of basic classical mechanics and relativity theory (special and general) and has been revised mainly for the purpose of adding exercises without worked solutions that were missing in the first edition. To retain the format of a readable, yet advanced introductory text that can serve as the companion text for a course in mechanics, the more than 100 new exercises on diverse topics are of moderate range; answers are given and occasionally hints are provided. As before, the text aims to cover the entire spectrum of theoretical mechanics from Newton to Einstein. The reader can observe how in the course of time, deeper and deeper insights were achieved with the development of the basic equations of Newton to those of Euler and Lagrange, and to the geodesic equations of space-time and Einstein's relativity. To include diverse problems, a small section on this topic has been added. 【目錄】 Chapter 1: Introduction Contents: Preface to Second Edition Preface to First Edition Introduction Recapitulation of Newtonian Mechanics The Lagrange Formalism The Canonical or Hamilton Formalism Symmetries and Transformations Looking Beyond Classical Mechanics Two-Body Central Forces Rigid Body Dynamics Small Oscillations and Stability Motivation of the Theory of Relativity A Simple Look at Phenomenological Consequences Aspects of Special Relativity Equation of Motion of a Particle in a Gravitational Field Tensor Calculus for Riemann Spaces Einstein's Equation of the Gravitational Field The Schwarzschild Solution Appendix A: Schwarzschild Orbit Solution Appendix B: Reissner–Nordstrom Metric Bibliography Index Readership: Undergraduate and graduate students who are interested in mechanics and relativity.

Einstein's General Theory of Relativity

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Einstein's general theory of relativity can be a notoriously difficult subject for students approaching it for the first time, with arcane mathematical concepts such as connection coefficients and tensors adorned with a forest of indices. This book is an elementary introduction to Einstein's theory and the physics of curved space-times that avoids these complications as much as possible. Its first half describes the physics of black holes, gravitational waves and the expanding Universe, without using tensors. Only in the second half are Einstein's field equations derived and used to explain the dynamical evolution of the early Universe and the creation of the first elements. Each chapter concludes with problem sets and technical mathematical details are given in the appendices. This short text is intended for undergraduate physics students who have taken courses in special relativity and advanced mechanics.

Conformal Methods in General Relativity

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This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this an ideal reference companion on the topic. This title, first published in 2016, has been reissued as an Open Access publication on Cambridge Core. Includes over seventy figures and diagrams to illustrate difficult concepts Extensive lists of further reading provide the reader with access into the important literature of the subject Encourages researchers in related areas to make use of the ideas discussed in their own research This title has been reissued as an Open Access publication on Cambridge Core