A Short Course in General Relativity (Google eBook)
Suitable for a one-semester course in general relativity for senior undergraduates or beginning graduate students, this text clarifies the mathematical aspects of Einstein's theory of relativity without sacrificing physical understanding. The text begins with an exposition of those aspects of tensor calculus and differential geometry needed for a proper treatment of the subject. The discussion then turns to the spacetime of general relativity and to geodesic motion. A brief consideration of the field equations is followed by a discussion of physics in the vicinity of massive objects, including an elementary treatment of black holes and rotating objects. The main text concludes with introductory chapters on gravitational radiation and cosmology. This new third edition has been updated to take account of fresh observational evidence and experiments. It includes new sections on the Kerr solution (in Chapter 4) and cosmological speeds of recession (in Chapter 6). A more mathematical treatment of tensors and manifolds, included in the 1st edition, but omitted in the 2nd edition, has been restored in an appendix. Also included are two additional appendixes – 'Special Relativity Review' and 'The Chinese Connection' - and outline solutions to all exercises and problems, making it especially suitable for private study.
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absolute derivative approximation axis basis vectors Cartesian coordinate system Cartesian coordinates change of coordinates connection coefficients constant contravariant vector coordinate curve coordinate system covariant vector defined differentiation direction distance dual basis energy equa Euclidean space example Exercise expression field equations flat spacetime follows function galaxy gauge geodesic equation given by equation gives gravitational field Hence implies inertial frames integral line element linear Lorentz manifold mass massive object matrix metric tensor metric tensor field natural basis Newtonian notation observer obtained orbit orthogonal parallel transport parallelly parameter parameterized path photon plane primed coordinates proper quantities radiation redshift relativistic result rotating satisfy Schwarzschild solution Section Show spatial special relativity spherical coordinates suffixes surface symmetric tangent space tangent vector tensor field test particle theory timelike tion transform according vector field vector space wavelength zero