Introduction to general relativity
A working knowledge of Einsteins 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.
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Particle on a TwoDimensional Surface
Curvilinear Coordinate Systems
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affine connection angular momentum baryon basis vectors black hole components conservation constant coordinate system coordinate transformation corresponding cosmology covariant derivative covariant divergence curve defined differential Einstein field equations energy-momentum tensor euclidian space expression Fetter and Walecka flat fluid four-dimensional four-vector frequency geodesic given by Eq global inertial laboratory gravitational field Hamilton's principle Hence identical illustrated in Fig indices inertial frame inertial laboratory frame infinitesimal displacement interval Lagrange's equations lagrangian light signal line element Lorentz transformation mass density matrix metric in Eq Minkowski space neutron star newtonian limit Note observed obtained orbit oscillations particle motion perihelion photon physical spatial distance Prob quantity r2 sin2 radial record keeper relation relativistic rest frame result Ricci tensor Riemann tensor Robertson-Walker metric scalar field Schwarzschild metric Schwarzschild radius Show simply solution space-time special relativity spherically symmetric tangent plane tangent space vanishes velocity