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Overview
This is a text on classical general relativity from a geometrical viewpoint. Introductory chapters are provided on algebra, topology and manifold theory, together with a chapter on the basic ideas of space-time manifolds and Einstein's theory. There is a detailed account of algebraic structures and tensor classification in general relativity and also of the relationships between the metric, connection and curvature structures on space-times. The latter includes chapters on holonomy and sectional curvature. An extensive study is presented of symmetries in general relativity, including isometries, homotheties, conformal symmetries and affine, projective and curvature collineations. Several general properties of such symmetries are studied and a preparatory section on transformation groups and on the properties of Lie algebras of vector fields on manifolds is provided.Synopsis
Hall (U. of Aberdeen) compiles the theoretical aspects of the literature on symmetries in general relativity that have been produced over the past few decades. He is not offering a textbook, he warns, but a study of certain aspects of four-dimensional Lorentzian differential geometry emphasizing the special requirements of Einstein's general theory of relativity. His main goal is to present a mathematical approach to symmetries and to the related topic of the connection and curvature structure of space-time, without paying much attention to attendant problems that worry mathematicians more than physicists. Annotation ©2004 Book News, Inc., Portland, OR