Differential Geometry And Relativity

Author : RichardL. Faber
Publisher : Routledge
Page : 150 pages
File Size : 54,9 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351455145

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Differential Geometry and Relativity Theory by RichardL. Faber Pdf

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 : M. Cahen,M. Flato
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 49,9 Mb
Release : 1976-12-31
Category : Gardening
ISBN : 9027707456

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Differential Geometry and Relativity by M. Cahen,M. Flato Pdf

On the sixtieth birthday of Andre Lichnerowicz a number of his friends, students, and coworkers decided to celebrate this event by preparing a jubilee volume of contributed articles in the two main fields of research marked by Lichnerowicz's work: differential geometry and mathematical physics. It was impossible to reflect in a single book the great variety of subjects tackled by Lichnerowicz. We hope that this book reflects some of the present trends of fields in which he worked, and some of the subjects to which he contributed in his long - and not yet finished - career. This career was very much marked by the influence of his masters, Elie Cartan who introduced him to research in mathematics, mainly in geometry and its relations with mathematical physics, and Georges Darmois who developed his interest in mechanics and physics, especially the theory of relativity and electromagnetism. This combination, and his personal talent, made him a natural scientific heir and continuator of the French mathematical physics school in the tradition of Henri Poincare. Some of his works would even be best qualified by a new field name, that of physical mathematics: branches of pure mathematics entirely motivated by physics.

Author : Lizhen Ji,Athanase Papadopoulos,Sumio Yamada
Publisher : Springer
Page : 647 pages
File Size : 50,6 Mb
Release : 2017-10-03
Category : Mathematics
ISBN : 9783319600390

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From Riemann to Differential Geometry and Relativity by Lizhen Ji,Athanase Papadopoulos,Sumio Yamada Pdf

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.

Author : Marcus Kriele
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 45,8 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540483540

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Spacetime by Marcus Kriele Pdf

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.

Author : RichardL. Faber
Publisher : Routledge
Page : 272 pages
File Size : 44,8 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351455152

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Differential Geometry and Relativity Theory by RichardL. Faber Pdf

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 : Tevian Dray
Publisher : CRC Press
Page : 324 pages
File Size : 42,7 Mb
Release : 2014-10-20
Category : Mathematics
ISBN : 9781466510005

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Differential Forms and the Geometry of General Relativity by Tevian Dray Pdf

Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity. The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible. The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.

Author : Paul Renteln
Publisher : Cambridge University Press
Page : 343 pages
File Size : 40,6 Mb
Release : 2014
Category : Science
ISBN : 9781107042193

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Manifolds, Tensors and Forms by Paul Renteln Pdf

Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.

Author : Chris J. Isham
Publisher : Allied Publishers
Page : 308 pages
File Size : 52,8 Mb
Release : 2002
Category : Geometry, Differential
ISBN : 8177643169

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Modern Differential Geometry for Physicists by Chris J. Isham Pdf

Author : Roger Penrose
Publisher : SIAM
Page : 80 pages
File Size : 54,7 Mb
Release : 1972-01-01
Category : Technology & Engineering
ISBN : 1611970601

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Techniques of Differential Topology in Relativity by Roger Penrose Pdf

Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.

Author : Dan A. Lee
Publisher : American Mathematical Soc.
Page : 361 pages
File Size : 54,5 Mb
Release : 2019-09-25
Category : Differential equations, Partial
ISBN : 9781470450816

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Geometric Relativity by Dan A. Lee Pdf

Many problems in general relativity are essentially geometric in nature, in the sense that they can be understood in terms of Riemannian geometry and partial differential equations. This book is centered around the study of mass in general relativity using the techniques of geometric analysis. Specifically, it provides a comprehensive treatment of the positive mass theorem and closely related results, such as the Penrose inequality, drawing on a variety of tools used in this area of research, including minimal hypersurfaces, conformal geometry, inverse mean curvature flow, conformal flow, spinors and the Dirac operator, marginally outer trapped surfaces, and density theorems. This is the first time these topics have been gathered into a single place and presented with an advanced graduate student audience in mind; several dozen exercises are also included. The main prerequisite for this book is a working understanding of Riemannian geometry and basic knowledge of elliptic linear partial differential equations, with only minimal prior knowledge of physics required. The second part of the book includes a short crash course on general relativity, which provides background for the study of asymptotically flat initial data sets satisfying the dominant energy condition.

Author : R.K. Sachs,H.-H. Wu
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461299035

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General Relativity for Mathematicians by R.K. Sachs,H.-H. Wu Pdf

This is a book about physics, written for mathematicians. The readers we have in mind can be roughly described as those who: I. are mathematics graduate students with some knowledge of global differential geometry 2. have had the equivalent of freshman physics, and find popular accounts of astrophysics and cosmology interesting 3. appreciate mathematical elarity, but are willing to accept physical motiva tions for the mathematics in place of mathematical ones 4. are willing to spend time and effort mastering certain technical details, such as those in Section 1. 1. Each book disappoints so me readers. This one will disappoint: 1. physicists who want to use this book as a first course on differential geometry 2. mathematicians who think Lorentzian manifolds are wholly similar to Riemannian ones, or that, given a sufficiently good mathematical back ground, the essentials of a subject !ike cosmology can be learned without so me hard work on boring detaiis 3. those who believe vague philosophical arguments have more than historical and heuristic significance, that general relativity should somehow be "proved," or that axiomatization of this subject is useful 4. those who want an encyclopedic treatment (the books by Hawking-Ellis [1], Penrose [1], Weinberg [1], and Misner-Thorne-Wheeler [I] go further into the subject than we do; see also the survey article, Sachs-Wu [1]). 5. mathematicians who want to learn quantum physics or unified fieId theory (unfortunateIy, quantum physics texts all seem either to be for physicists, or merely concerned with formaI mathematics).

Author : Peter Szekeres
Publisher : Cambridge University Press
Page : 620 pages
File Size : 55,6 Mb
Release : 2004-12-16
Category : Mathematics
ISBN : 0521829607

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A Course in Modern Mathematical Physics by Peter Szekeres Pdf

This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.

Author : John K. Beem,Advances in Differential Geometry Beemfest,Stamatis A. Dostoglou,Paul E. Ehrlich
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 54,7 Mb
Release : 2004
Category : General relativity (Physics)
ISBN : 9780821835395

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Advances in Differential Geometry and General Relativity by John K. Beem,Advances in Differential Geometry Beemfest,Stamatis A. Dostoglou,Paul E. Ehrlich Pdf

This volume consists of expanded versions of invited lectures given at The Beemfest: Advances in Differential Geometry and General Relativity (University of Missouri-Columbia) on the occasion of Professor John K. Beem's retirement. The articles address problems in differential geometry in general and in particular, global Lorentzian geometry, Finsler geometry, causal boundaries, Penrose's cosmic censorship hypothesis, the geometry of differential operators with variable coefficients on manifolds, and asymptotically de Sitter spacetimes satisfying Einstein's equations with positive cosmological constant. The book is suitable for graduate students and research mathematicians interested in differential geometry.

Author : James J. Callahan
Publisher : Springer Science & Business Media
Page : 474 pages
File Size : 51,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9781475767360

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The Geometry of Spacetime by James J. Callahan Pdf

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.

Author : Stephen C. Newman
Publisher : John Wiley & Sons
Page : 656 pages
File Size : 43,7 Mb
Release : 2019-07-30
Category : Mathematics
ISBN : 9781119517535

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Semi-Riemannian Geometry by Stephen C. Newman Pdf

An introduction to semi-Riemannian geometry as a foundation for general relativity Semi-Riemannian Geometry: The Mathematical Language of General Relativity is an accessible exposition of the mathematics underlying general relativity. The book begins with background on linear and multilinear algebra, general topology, and real analysis. This is followed by material on the classical theory of curves and surfaces, expanded to include both the Lorentz and Euclidean signatures. The remainder of the book is devoted to a discussion of smooth manifolds, smooth manifolds with boundary, smooth manifolds with a connection, semi-Riemannian manifolds, and differential operators, culminating in applications to Maxwell’s equations and the Einstein tensor. Many worked examples and detailed diagrams are provided to aid understanding. This book will appeal especially to physics students wishing to learn more differential geometry than is usually provided in texts on general relativity.