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Author: Barrett O'Neill
Publisher: Courier Corporation
Published: 2014-01-15
Total Pages: 404
ISBN-13: 0486783111
DOWNLOAD EBOOKSuitable for advanced undergraduates and graduate students of mathematics as well as for physicists, this unique monograph and self-contained treatment constitutes an introduction to modern techniques in differential geometry. 1995 edition.
Author: Barrett O'Neill
Publisher: Courier Corporation
Published: 2014-03-19
Total Pages: 404
ISBN-13: 0486493423
DOWNLOAD EBOOKSuitable for advanced undergraduates and graduate students of mathematics as well as for physicists, this unique monograph and self-contained treatment constitutes an introduction to modern techniques in differential geometry. 1995 edition.
Author: Derek J. Raine
Publisher: Imperial College Press
Published: 2010
Total Pages: 211
ISBN-13: 1848163827
DOWNLOAD EBOOKThis introduction to the fascinating subject of black holes fills a significant gap in the literature which exists between popular, non-mathematical expositions and advanced textbooks at the research level. It is designed for advanced undergraduates and first year postgraduates as a useful stepping-stone to the advanced literature. The book provides an accessible introduction to the exact solutions of Einstein's vacuum field equations describing spherical and axisymmetric (rotating) black holes. The geometry and physical properties of these spacetimes are explored through the motion of particles and light. The use of different coordinate systems, maximal extensions and Penrose diagrams is explained. The association of the surface area of a black hole with its entropy is discussed and it is shown that with the introduction of quantum mechanics black holes cease to be black and can radiate. This result allows black holes to satisfy the laws of thermodynamics and thus be consistent with the rest of physics. In this new edition the problems in each chapter have been revised and solutions are provided. The text has been expanded to include new material on wormholes and clarify various other issues.
Author: Subrahmanyan Chandrasekhar
Publisher: Oxford University Press
Published: 1998
Total Pages: 676
ISBN-13: 9780198503705
DOWNLOAD EBOOKPart of the reissued Oxford Classic Texts in the Physical Sciences series, this book was first published in 1983, and has swiftly become one of the great modern classics of relativity theory. It represents a personal testament to the work of the author, who spent several years writing and working-out the entire subject matter. The theory of black holes is the most simple and beautiful consequence of Einstein's relativity theory. At the time of writing there was no physical evidence for the existence of these objects, therefore all that Professor Chandrasekhar used for their construction were modern mathematical concepts of space and time. Since that time a growing body of evidence has pointed to the truth of Professor Chandrasekhar's findings, and the wisdom contained in this book has become fully evident.
Author: Valeri P. Frolov
Publisher: Oxford University Press
Published: 2011-09-22
Total Pages: 505
ISBN-13: 0199692297
DOWNLOAD EBOOKWhat is a black hole? How many of them are in our Universe? Can black holes be created in a laboratory or in particle colliders? Can objects similar to black holes be used for space and time travel? This book discusses these and many other questions providing the reader with the tools required to explore the Black Hole Land independently.
Author: David L. Wiltshire
Publisher: Cambridge University Press
Published: 2009-01-22
Total Pages: 0
ISBN-13: 0521885124
DOWNLOAD EBOOKUnique, comprehensive overview for researchers and graduate students in observational and theoretical astrophysics, general relativity, and high-energy physics.
Author: Piotr T. Chruściel
Publisher:
Published: 2020
Total Pages: 404
ISBN-13: 0198855419
DOWNLOAD EBOOKBlack holes present one of the most fascinating predictions of Einstein's general relativity, with strong evidence of their existence through observations of many means. The book provides a wide background to the current research on all mathematical aspects of the geometry of black hole spacetimes.
Author: Barrett O'Neill
Publisher: Academic Press
Published: 1983-07-29
Total Pages: 483
ISBN-13: 0080570577
DOWNLOAD EBOOKThis 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: Tevian Dray
Publisher: CRC Press
Published: 2012-07-02
Total Pages: 151
ISBN-13: 1466510471
DOWNLOAD EBOOKThe Geometry of Special Relativity provides an introduction to special relativity that encourages readers to see beyond the formulas to the deeper geometric structure. The text treats the geometry of hyperbolas as the key to understanding special relativity. This approach replaces the ubiquitous γ symbol of most standard treatments with the appropriate hyperbolic trigonometric functions. In most cases, this not only simplifies the appearance of the formulas, but also emphasizes their geometric content in such a way as to make them almost obvious. Furthermore, many important relations, including the famous relativistic addition formula for velocities, follow directly from the appropriate trigonometric addition formulas. The book first describes the basic physics of special relativity to set the stage for the geometric treatment that follows. It then reviews properties of ordinary two-dimensional Euclidean space, expressed in terms of the usual circular trigonometric functions, before presenting a similar treatment of two-dimensional Minkowski space, expressed in terms of hyperbolic trigonometric functions. After covering special relativity again from the geometric point of view, the text discusses standard paradoxes, applications to relativistic mechanics, the relativistic unification of electricity and magnetism, and further steps leading to Einstein’s general theory of relativity. The book also briefly describes the further steps leading to Einstein’s general theory of relativity and then explores applications of hyperbola geometry to non-Euclidean geometry and calculus, including a geometric construction of the derivatives of trigonometric functions and the exponential function.
Author: Sean M. Carroll
Publisher: Cambridge University Press
Published: 2019-08-08
Total Pages: 529
ISBN-13: 1108488390
DOWNLOAD EBOOKAn accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
