General Relativity: An Introduction for Physicists (Google eBook)
General Relativity: An Introduction for Physicists provides a clear mathematical introduction to Einstein's theory of general relativity. It presents a wide range of applications of the theory, concentrating on its physical consequences. After reviewing the basic concepts, the authors present a clear and intuitive discussion of the mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are then used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is then introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle. Written for advanced undergraduate and graduate students, this approachable textbook contains over 300 exercises to illuminate and extend the discussion in the text.
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这本书不错, 很大篇幅在宇宙学应用上, 很基本, 公式也很全!
4-velocity angular momentum basis vectors black hole Cartesian coordinates Cartesian inertial circular orbit comoving connection coefficients consider constant contravariant components coordinate radius coordinate transformation corresponding cosmic covariant components covariant derivative curvature tensor curve defined denote density differential discussion distance Einstein electromagnetic field emitted energy energy–momentum tensor equation of motion equatorial plane ergoregion Euclidean space event horizon example expression field equations Figure function galaxy geodesic equations given gravitational field gravitational wave Hence show inertial frame inflation integral Kerr metric Lagrangian line element linearised Lorenz gauge condition manifold mass massive particle metric tensor Minkowski spacetime Newtonian non-zero null observer obtain perturbation photon physical radial redshift region respect result Ricci tensor rotating satisfy scalar field scale factor Schwarzschild geometry Schwarzschild metric Section sin2 d2 singularity solution spacelike spherical stationary surface symmetric theory timelike trajectory universe velocity worldline zero
Page 23 - For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise — assuming...
Page 23 - ... draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighborhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighborhood of the magnet. In the conductor, however...
Page 23 - It is known that Maxwell's electrodynamics — as usually understood at the present time — when applied to moving bodies, leads to assymmetries which do not appear to be inherent in the phenomena. Take for example the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet ; whereas the customary view draws a sharp distinction...