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

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书目名称Spacetime, Geometry and Gravitation
编辑Pankaj Sharan
视频video
概述Physically intuitive, but mathematically rigorous writing style.Early introduction to geometric quantities allows students to learn simpler topics in general relativity (Newtonian limit, Schwarzschild
丛书名称Progress in Mathematical Physics
图书封面Titlebook: Spacetime, Geometry and Gravitation;  Pankaj Sharan Textbook 2009 Birkhäuser Basel 2009 Christoffel symbol.Friedman equation.Gravity.Kerr s
描述This is an introductory book on the general theory of relativity based partly on lectures given to students of M.Sc. Physics at my university. The book is divided into three parts. The ?rst part is a preliminary course on general relativity with minimum preparation. The second part builds the ma- ematical background and the third part deals with topics where mathematics developed in the second part is needed. The ?rst chapter gives a general background and introduction. This is f- lowed by an introduction to curvature through Gauss’ Theorema Egregium. This theorem expresses the curvature of a two-dimensional surface in terms of intrinsic quantitiesrelatedtothein?nitesimaldistancefunctiononthesurface.Thestudent isintroducedtothemetrictensor,Christo?elsymbolsandRiemanncurvaturet- sor by elementary methods in the familiar and visualizable case of two dimensions. This early introduction to geometric quantities equips a student to learn simpler topics in general relativity like the Newtonian limit, red shift, the Schwarzschild solution, precession of the perihelion and bending of light in a gravitational ?eld. Part II (chapters 5 to 10) is an introduction to Riemannian geometry as - qui
出版日期Textbook 2009
关键词Christoffel symbol; Friedman equation; Gravity; Kerr solution; Relativity; Riemannian geometry; Schwarzsch
版次1
doihttps://doi.org/10.1007/978-3-7643-9971-9
isbn_ebook978-3-7643-9971-9Series ISSN 1544-9998 Series E-ISSN 2197-1846
issn_series 1544-9998
copyrightBirkhäuser Basel 2009
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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.
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