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Differential Geometry And Relativity Theory

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Differential Geometry And Relativity Theory

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Author : Richard L. Faber
language : en
Publisher: CRC Press
Release Date : 1983-05-26

Differential Geometry And Relativity Theory written by Richard L. Faber and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-05-26 with Mathematics categories.

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

Spacetime

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Author : Marcus Kriele
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-01

Spacetime written by Marcus Kriele and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Science categories.

One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-’ We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities". add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one,should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.

Differential Geometry And Relativity Theory

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Author : RichardL. Faber
language : en
Publisher: Routledge
Release Date : 2017-10-19

Differential Geometry And Relativity Theory written by RichardL. Faber and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.

From Riemann To Differential Geometry And Relativity

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Author : Lizhen Ji
language : en
Publisher: Springer
Release Date : 2017-10-03

From Riemann To Differential Geometry And Relativity written by Lizhen Ji and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-03 with Mathematics categories.

This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

Differential Geometry Gauge Theories And Gravity

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Author : M. Göckeler
language : en
Publisher: Cambridge University Press
Release Date : 1989-07-28

Differential Geometry Gauge Theories And Gravity written by M. Göckeler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-07-28 with Mathematics categories.

Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.

The Geometry Of Spacetime

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Author : James J. Callahan
language : en
Publisher: Springer Science & Business Media
Release Date : 2000

The Geometry Of Spacetime written by James J. Callahan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Computers categories.

Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.

The Physical And Mathematical Foundations Of The Theory Of Relativity

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Author : Antonio Romano
language : en
Publisher: Springer Nature
Release Date : 2019-09-25

The Physical And Mathematical Foundations Of The Theory Of Relativity written by Antonio Romano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-25 with Science categories.

This unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications. The transitions from classical mechanics to special relativity and then to general relativity are explored in detail as well, helping readers to gain a more profound and nuanced understanding of the theory as a whole. After reviewing the fundamentals of differential geometry and classical mechanics, the text introduces special relativity, first using the physical approach proposed by Einstein and then via Minkowski’s mathematical model. The authors then address the relativistic thermodynamics of continua and electromagnetic fields in matter – topics which are normally covered only very briefly in other treatments – in the next two chapters. The text then turns to a discussion of general relativity by means of the authors’ unique critical approach, underlining the difficulty of recognizing the physical meaning of some statements, such as the physical meaning of coordinates and the derivation of physical quantities from those of space-time. Chapters in this section cover the model of space-time proposed by Schwarzschild; black holes; the Friedman equations and the different cosmological models they describe; and the Fermi-Walker derivative. Well-suited for graduate students in physics and mathematics who have a strong foundation in real analysis, classical mechanics, and general physics, this textbook is appropriate for a variety of graduate-level courses that cover topics in relativity. Additionally, it will interest physicists and other researchers who wish to further study the subtleties of these theories and understand the contemporary scholarly discussions surrounding them.

Modern Differential Geometry For Physicists

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Author : Chris J. Isham
language : en
Publisher: Allied Publishers
Release Date : 2002

Modern Differential Geometry For Physicists written by Chris J. Isham and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Geometry, Differential categories.

Differential Forms And The Geometry Of General Relativity

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Author : Tevian Dray
language : en
Publisher: A K PETERS
Release Date : 2024-10-14

Differential Forms And The Geometry Of General Relativity written by Tevian Dray and has been published by A K PETERS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-14 with Mathematics categories.

Requiring little more than calculus and some linear algebra, this book provides readers with a coherent path to understanding relativity. It helps readers learn just enough differential geometry to grasp the basics of general relativity. The first half of the book describes

The Geometry Of Special Relativity

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Author : Tevian Dray
language : en
Publisher: CRC Press
Release Date : 2012-07-02

The Geometry Of Special Relativity written by Tevian Dray and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-02 with Mathematics categories.

The 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.

Differential Geometry And Relativity Theory

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