Introduction to General RelativityA working knowledge of Einstein's theory of general relativity is an essential tool for every physicist today. This self-contained book is an introductory text on the subject aimed at first-year graduate students, or advanced undergraduates, in physics that assumes only a basic understanding of classical Lagrangian mechanics. The mechanics problem of a point mass constrained to move without friction on a two-dimensional surface of arbitrary shape serves as a paradigm for the development of the mathematics and physics of general relativity. After reviewing special relativity, the basic principles of general relativity are presented, and the most important applications are discussed. The final special topics section guides the reader through a few important areas of current research.This book will allow the reader to approach the more advanced texts and monographs, as well as the continual influx of fascinating new experimental results, with a deeper understanding and sense of appreciation. |
Contents
Introduction | 1 |
Particle on a TwoDimensional Surface | 9 |
Curvilinear Coordinate Systems | 27 |
Particle on a TwoDimensional SurfaceRevisited | 43 |
Some Tensor Analysis | 51 |
Special Relativity | 87 |
General Relativity | 123 |
Precession of Perihelion | 155 |
Neutron Stars | 181 |
Cosmology | 217 |
Gravitational Radiation | 241 |
Special Topics | 263 |
Problems | 281 |
Appendix A Reduction of gµν δRµν to covariant divergences | 321 |
Appendix B RobertsonWalker Metric with k 0 | 325 |
Gravitational Redshift | 173 |
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Introduction to General Relativity, Black Holes, and Cosmology Yvonne Choquet-Bruhat Limited preview - 2014 |
Common terms and phrases
actual assume basis vectors becomes chapter components condition connection conservation Consider constant coordinates corresponding covariant curvature curve defined density depends derivative described determinant direction discussion displacement distance effective Einstein element energy equations euclidian event example expanded expression field field equations first flat follows force frequency geodesic given gives global gravitational Hence identical indices inertial infinitesimal interval laboratory frame lagrangian leads light limit Lorentz Lorentz metric mass matrix matter motion moving neutron newtonian Note observed obtained origin particle physical position present principle Prob problem proper provides quantity radial relation relativity rest result Ricci tensor scalar Schwarzschild metric Show simply solution space spatial special relativity spherically star surface symmetric takes tangent plane tensor theory transformation vanishes velocity wave write