Geometric Relativity

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Geometric Relativity

Dan A. Lee
Geometric Relativity Book PDF

Author : Dan A. Lee
Publisher : American Mathematical Soc.
Page : 361 pages
File Size : 46,8 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.

Geometric Relativity

Dan A. Lee
Geometric Relativity Book PDF

Author : Dan A. Lee
Publisher : American Mathematical Society
Page : 377 pages
File Size : 45,8 Mb
Release : 2021-12-20
Category : Mathematics
ISBN : 9781470466237

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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.

Relativity and Geometry

Roberto Torretti
Relativity and Geometry Book PDF

Author : Roberto Torretti
Publisher : Elsevier
Page : 408 pages
File Size : 49,7 Mb
Release : 2014-05-20
Category : Science
ISBN : 9781483147376

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Relativity and Geometry by Roberto Torretti Pdf

Relativity and Geometry aims to elucidate the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phases of relativity. The book contains seven chapters and a mathematical appendix. The first two chapters review a historical background of relativity. Chapter 3 centers on Einstein's first Relativity paper of 1905. Subsequent chapter presents the Minkowskian formulation of special relativity. Chapters 5 and 6 deal with Einstein's search for general relativity from 1907 to 1915, as well as some aspects and subsequent developments of the theory. The last chapter explores the concept of simultaneity, geometric conventionalism, and a few other questions concerning space time structure, causality, and time.

Geometric Theory of Generalized Functions with Applications to General Relativity

Michael Grosser
Geometric Theory of Generalized Functions with Applications to General Relativity Book PDF

Author : Michael Grosser
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 53,7 Mb
Release : 2001-11-30
Category : Mathematics
ISBN : 1402001452

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Geometric Theory of Generalized Functions with Applications to General Relativity by Michael Grosser Pdf

This work provides the first comprehensive introduction to the nonlinear theory of generalized functions (in the sense of Colombeau's construction) on differentiable manifolds. Particular emphasis is laid on a diffeomorphism invariant geometric approach to embedding the space of Schwartz distributions into algebras of generalized functions. The foundations of a `nonlinear distributional geometry' are developed, supplying a solid base for an increasing number of applications of algebras of generalized functions to questions of a primarily geometric mature, in particular in mathematical physics. Applications of the resulting theory to symmetry group analysis of differential equations and the theory of general relativity are presented in separate chapters. These features distinguish the present volume from earlier introductory texts and monographs on the subject. Audience: The book will be of interest to graduate students as well as to researchers in functional analysis, partial differential equations, differential geometry, and mathematical physics.

Geometry, Relativity and the Fourth Dimension

Rudolf Rucker
Geometry Relativity and the Fourth Dimension Book PDF

Author : Rudolf Rucker
Publisher : Courier Corporation
Page : 159 pages
File Size : 41,9 Mb
Release : 2012-06-08
Category : Science
ISBN : 9780486140339

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Geometry, Relativity and the Fourth Dimension by Rudolf Rucker Pdf

Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.

The Geometry of Special Relativity

Tevian Dray
The Geometry of Special Relativity Book PDF

Author : Tevian Dray
Publisher : CRC Press
Page : 151 pages
File Size : 41,9 Mb
Release : 2012-07-02
Category : Mathematics
ISBN : 9781466510470

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The Geometry of Special Relativity by Tevian Dray Pdf

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 Forms and the Geometry of General Relativity

Tevian Dray
Differential Forms and the Geometry of General Relativity Book PDF

Author : Tevian Dray
Publisher : CRC Press
Page : 324 pages
File Size : 53,9 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.

The Geometry of Spacetime

James J. Callahan
The Geometry of Spacetime Book PDF

Author : James J. Callahan
Publisher : Springer Science & Business Media
Page : 474 pages
File Size : 53,9 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.

Geometry: from Isometries to Special Relativity

Nam-Hoon Lee
Geometry from Isometries to Special Relativity Book PDF

Author : Nam-Hoon Lee
Publisher : Springer Nature
Page : 264 pages
File Size : 43,5 Mb
Release : 2020-04-28
Category : Mathematics
ISBN : 9783030421014

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Geometry: from Isometries to Special Relativity by Nam-Hoon Lee Pdf

This textbook offers a geometric perspective on special relativity, bridging Euclidean space, hyperbolic space, and Einstein’s spacetime in one accessible, self-contained volume. Using tools tailored to undergraduates, the author explores Euclidean and non-Euclidean geometries, gradually building from intuitive to abstract spaces. By the end, readers will have encountered a range of topics, from isometries to the Lorentz–Minkowski plane, building an understanding of how geometry can be used to model special relativity. Beginning with intuitive spaces, such as the Euclidean plane and the sphere, a structure theorem for isometries is introduced that serves as a foundation for increasingly sophisticated topics, such as the hyperbolic plane and the Lorentz–Minkowski plane. By gradually introducing tools throughout, the author offers readers an accessible pathway to visualizing increasingly abstract geometric concepts. Numerous exercises are also included with selected solutions provided. Geometry: from Isometries to Special Relativity offers a unique approach to non-Euclidean geometries, culminating in a mathematical model for special relativity. The focus on isometries offers undergraduates an accessible progression from the intuitive to abstract; instructors will appreciate the complete instructor solutions manual available online. A background in elementary calculus is assumed.

Spacetime and Geometry

Sean M. Carroll
Spacetime and Geometry Book PDF

Author : Sean M. Carroll
Publisher : Cambridge University Press
Page : 529 pages
File Size : 54,6 Mb
Release : 2019-08-08
Category : Science
ISBN : 9781108488396

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Spacetime and Geometry by Sean M. Carroll Pdf

An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.

Differential Geometry and Relativity Theory

RichardL. Faber
Differential Geometry and Relativity Theory Book PDF

Author : RichardL. Faber
Publisher : Routledge
Page : 150 pages
File Size : 47,9 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

General Relativity

Malcolm Ludvigsen
General Relativity Book PDF

Author : Malcolm Ludvigsen
Publisher : Cambridge University Press
Page : 234 pages
File Size : 48,9 Mb
Release : 1999-05-28
Category : Mathematics
ISBN : 052163976X

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General Relativity by Malcolm Ludvigsen Pdf

Solutions and hints to selected exercises

Differential Geometry and Relativity Theory

RichardL. Faber
Differential Geometry and Relativity Theory Book PDF

Author : RichardL. Faber
Publisher : Routledge
Page : 272 pages
File Size : 51,8 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

The Geometry of Special Relativity

Tevian Dray
The Geometry of Special Relativity Book PDF

Author : Tevian Dray
Publisher : CRC Press
Page : 197 pages
File Size : 55,7 Mb
Release : 2021-06-10
Category : Mathematics
ISBN : 9781315160702

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The Geometry of Special Relativity by Tevian Dray Pdf

This unique book presents a particularly beautiful way of looking at special relativity. The author encourages students to see beyond the formulas to the deeper structure. The unification of space and time introduced by Einstein’s special theory of relativity is one of the cornerstones of the modern scientific description of the universe. Yet the unification is counterintuitive because we perceive time very differently from space. Even in relativity, time is not just another dimension, it is one with different properties The book treats the geometry of hyperbolas as the key to understanding special relativity. The author simplifies the formulas and emphasizes their geometric content. Many important relations, including the famous relativistic addition formula for velocities, then follow directly from the appropriate (hyperbolic) trigonometric addition formulas. Prior mastery of (ordinary) trigonometry is sufficient for most of the material presented, although occasional use is made of elementary differential calculus, and the chapter on electromagnetism assumes some more advanced knowledge. Changes to the Second Edition The treatment of Minkowski space and spacetime diagrams has been expanded. Several new topics have been added, including a geometric derivation of Lorentz transformations, a discussion of three-dimensional spacetime diagrams, and a brief geometric description of "area" and how it can be used to measure time and distance. Minor notational changes were made to avoid conflict with existing usage in the literature. Table of Contents Preface 1. Introduction. 2. The Physics of Special Relativity. 3. Circle Geometry. 4. Hyperbola Geometry. 5. The Geometry of Special Relativity. 6. Applications. 7. Problems III. 8. Paradoxes. 9. Relativistic Mechanics. 10. Problems II. 11. Relativistic Electromagnetism. 12. Problems III. 13. Beyond Special Relativity. 14. Three-Dimensional Spacetime Diagrams. 15. Minkowski Area via Light Boxes. 16. Hyperbolic Geometry. 17. Calculus. Bibliography. Author Biography Tevian Dray is a Professor of Mathematics at Oregon State University. His research lies at the interface between mathematics and physics, involving differential geometry and general relativity, as well as nonassociative algebra and particle physics; he also studies student understanding of "middle-division" mathematics and physics content. Educated at MIT and Berkeley, he held postdoctoral positions in both mathematics and physics in several countries prior to coming to OSU in 1988. Professor Dray is a Fellow of the American Physical Society for his work in relativity, and an award-winning teacher.

General Relativity for Mathematicians

R.K. Sachs,H.-H. Wu
General Relativity for Mathematicians Book PDF

Author : R.K. Sachs,H.-H. Wu
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 40,9 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).