Author : F. de Felice
Publisher : Cambridge University Press
Page : 466 pages
File Size : 23,73 MB
Release : 1992-03-27
Category : Mathematics
ISBN : 9780521429085
This is a self-contained exposition of general relativity with emphasis given to tetrad and spinor structures and physical measurement on curved manifolds.
Author : Barrett O'Neill
Publisher : Academic Press
Page : 483 pages
File Size : 41,27 MB
Release : 1983-07-29
Category : Mathematics
ISBN : 0080570577
This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.
Author : C. J. S. Clarke
Publisher : Cambridge University Press
Page : 196 pages
File Size : 28,22 MB
Release : 1993
Category : Science
ISBN : 9780521437967
The different possible singularities are defined and the mathematical methods needed to extend the space-time are described in detail in this book. Results obtained (many appearing here for the first time) show that singularities are associated with a lack of smoothness in the Riemann tensor.
Author : Brian P. Dolan
Publisher : Cambridge University Press
Page : 215 pages
File Size : 15,9 MB
Release : 2023-06-30
Category : Science
ISBN : 1009263714
Einstein's general theory of relativity can be a notoriously difficult subject for students approaching it for the first time, with arcane mathematical concepts such as connection coefficients and tensors adorned with a forest of indices. This book is an elementary introduction to Einstein's theory and the physics of curved space-times that avoids these complications as much as possible. Its first half describes the physics of black holes, gravitational waves and the expanding Universe, without using tensors. Only in the second half are Einstein's field equations derived and used to explain the dynamical evolution of the early Universe and the creation of the first elements. Each chapter concludes with problem sets and technical mathematical details are given in the appendices. This short text is intended for undergraduate physics students who have taken courses in special relativity and advanced mechanics.
Author : Sean M. Carroll
Publisher : Cambridge University Press
Page : 529 pages
File Size : 41,24 MB
Release : 2019-08-08
Category : Science
ISBN : 1108488390
An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
Author : Anadi Jiban Das
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 27,44 MB
Release : 2007-10-05
Category : Science
ISBN : 0387694692
Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.
Author : RichardL. Faber
Publisher : Routledge
Page : 280 pages
File Size : 24,18 MB
Release : 2017-10-19
Category : Mathematics
ISBN : 1351455141
Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force. Uniting differential geometry and both special and generalrelativity in a single source, this easy-to-understand text opens the general theory of relativityto mathematics majors having a backgr.ound only in multivariable calculus and linearalgebra.The book offers a broad overview of the physical foundations and mathematical details ofrelativity, and presents concrete physical interpretations of numerous abstract concepts inRiemannian geometry. The work is profusely illustrated with diagrams aiding in the understandingof proofs and explanations. Appendices feature important material on vectoranalysis and hyperbolic functions.Differential Geometry and Relativity Theory: An Introduction serves as the ideal textfor high-level undergraduate couues in mathematics and physics, and includes a solutionsmanual augmenting classroom study. It is an invaluable reference for mathematicians interestedin differential and IUemannian geometry, or the special and general theories ofrelativity
Author : Bernard Schutz
Publisher : Cambridge University Press
Page : 411 pages
File Size : 25,95 MB
Release : 2009-05-14
Category : Science
ISBN : 0521887054
Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.
Author : Robert M. Wald
Publisher : University of Chicago Press
Page : 507 pages
File Size : 31,52 MB
Release : 2010-05-15
Category : Science
ISBN : 0226870375
"Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement "Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today
Author : Shlomo Sternberg
Publisher : Courier Corporation
Page : 418 pages
File Size : 45,75 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 0486292711
Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.
