Titlebook: Spacetime, Geometry and Gravitation; Pankaj Sharan Textbook 2009 Birkh?user Basel 2009 Christoffel symbol.Friedman equation.Gravity.Kerr s

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intuition

General Features of Spacetimes. As the metric is non-degenerate, there can be no zero eigenvalues. This statement is independent of coordinate system chosen. The actual numerical values of eigenvalues of the tensor matrix may vary from one coordinate system to another but the number of eigenvalues of positive sign and of negative sign is the same.

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Introductionlopments. According to the theory spacetime is a Riemannian space whose metric .. determines the gravitational field.. The .. governs the gravitational field. In this equation the quantities .., . are functions of the metric .. and its various derivatives and .. on the right-hand side are determined

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Elementary Differential Geometryw chapters we develop the necessary background with emphasis on tools necessary for a physicist. This introduction is not rigorous from a mathematician’s point of view. We would assume that these manifolds have all the nice mathematical properties (Hausdorff nature, paracompactness etc.) which are n

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Weak Gravitational Fieldsredictions which are startling. For example a spherical mass rotating slowly about an axis will “drag inertial frames” so that the spin of a gyroscope far from the mass will precess. Another prediction of the general theory of relativity is that perturbations of the metric . propagate as waves.