Mathematical Foundation Of The General Theory Of Relativity

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Mathematical Foundation of the General Theory of Relativity

Albert Einstein
Mathematical Foundation of the General Theory of Relativity Book PDF

Author : Albert Einstein
Publisher : Blurb
Page : 96 pages
File Size : 46,8 Mb
Release : 2021-07-19
Category : Electronic
ISBN : 1006727140

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Mathematical Foundation of the General Theory of Relativity by Albert Einstein Pdf

The theory which is sketched in the following pages forms the most wide-going generalization conceivable of what is at present known as "the theory of Relativity;" this latter theory I differentiate from the former "Special Relativity theory," and suppose it to be known. The generalization of the Relativity theory has been made much easier through the form given to the special Relativity theory by Minkowski, which mathematician was the first to recognize clearly the formal equivalence of the space like and time-like co-ordinates, and who made use of it in the building up of the theory. The mathematical apparatus useful for the general relativity theory, lay already complete in the "Absolute Differential Calculus", which were based on the researches of GAUSS, RIEMANN and CHRISTOFFEL on the non-Euclidean manifold, and which have been shaped into a system by RICCI and LEVI-CIVITA, and already applied to the problems of theoretical physics. I have in part B of this communication developed in the simplest and clearest manner, all the supposed mathematical auxiliaries, not known to Physicists, which will be useful for our purpose, so that, a study of the mathematical literature is not necessary for an understanding of this paper. Finally in this place I thank my friend GROSSMANN, by whose help I was not only spared the study of the mathematical literature pertinent to this subject, but who also aided me in the researches on the field equations of gravitation.

The General Theory of Relativity

Farook Rahaman
The General Theory of Relativity Book PDF

Author : Farook Rahaman
Publisher : Cambridge University Press
Page : 427 pages
File Size : 43,9 Mb
Release : 2021-09-30
Category : Science
ISBN : 9781108837996

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The General Theory of Relativity by Farook Rahaman Pdf

Discusses the general theory of relativity, Lie derivatives, rotating black holes, with a focus on basics of cosmology and astrophysics.

The Physical and Mathematical Foundations of the Theory of Relativity

Antonio Romano,Mario Mango Furnari
The Physical and Mathematical Foundations of the Theory of Relativity Book PDF

Author : Antonio Romano,Mario Mango Furnari
Publisher : Springer Nature
Page : 496 pages
File Size : 52,6 Mb
Release : 2019-09-25
Category : Science
ISBN : 9783030272371

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The Physical and Mathematical Foundations of the Theory of Relativity by Antonio Romano,Mario Mango Furnari Pdf

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.

Foundations of General Relativity

Klaas Landsman
Foundations of General Relativity Book PDF

Author : Klaas Landsman
Publisher : Radboud University Press
Page : 394 pages
File Size : 54,8 Mb
Release : 2021-10-08
Category : Science
ISBN : 9789083178929

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Foundations of General Relativity by Klaas Landsman Pdf

This book, dedicated to Roger Penrose, is a second, mathematically oriented course in general relativity. It contains extensive references and occasional excursions in the history and philosophy of gravity, including a relatively lengthy historical introduction. The book is intended for all students of general relativity of any age and orientation who have a background including at least first courses in special and general relativity, differential geometry, and topology. The material is developed in such a way that through the last two chapters the reader may acquire a taste of the modern mathematical study of black holes initiated by Penrose, Hawking, and others, as further influenced by the initial-value or PDE approach to general relativity. Successful readers might be able to begin reading research papers on black holes, especially in mathematical physics and in the philosophy of physics. The chapters are: Historical introduction, General differential geometry, Metric differential geometry, Curvature, Geodesics and causal structure, The singularity theorems of Hawking and Penrose, The Einstein equations, The 3+1 split of space-time, Black holes I: Exact solutions, and Black holes II: General theory. These are followed by two appendices containing background on Lie groups, Lie algebras, & constant curvature, and on Formal PDE theory.

The General Theory of Relativity

Anadijiban Das,Andrew DeBenedictis
The General Theory of Relativity Book PDF

Author : Anadijiban Das,Andrew DeBenedictis
Publisher : Springer Science & Business Media
Page : 694 pages
File Size : 45,9 Mb
Release : 2012-06-26
Category : Science
ISBN : 9781461436584

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The General Theory of Relativity by Anadijiban Das,Andrew DeBenedictis Pdf

The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: tensor analysis the special theory of relativity the general theory of relativity and Einstein’s field equations spherically symmetric solutions and experimental confirmations static and stationary space-time domains black holes cosmological models algebraic classifications and the Newman-Penrose equations the coupled Einstein-Maxwell-Klein-Gordon equations appendices covering mathematical supplements and special topics Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars. Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland, Jadavpur University, India, Carnegie-Mellon University, USA, and Simon Fraser University, Canada. His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory. Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fraser University, Canada, and is also a member of The Pacific Institute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity.

Theory of Relativity

Albert Einstein
Theory of Relativity Book PDF

Author : Albert Einstein
Publisher : CreateSpace
Page : 50 pages
File Size : 50,9 Mb
Release : 2015-06-02
Category : Electronic
ISBN : 1514182734

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Theory of Relativity by Albert Einstein Pdf

Theory of Relativity: The Foundation by Albert Einstein. The theory which is sketched in the following pages forms the most wide-going generalization conceivable of what is at present known as "the theory of Relativity;" this latter theory I differentiate from the former "Special Relativity theory," and suppose it to be known. The generalization of the Relativity theory has been made much easier through the form given to the special Relativity theory by Minkowski, which mathematician was the first to recognize clearly the formal equivalence of the space like and time-like co-ordinates, and who made use of it in the building up of the theory. The mathematical apparatus useful for the general relativity theory, lay already complete in the "Absolute Differential Calculus," which were based on the researches of GAUSS, RIEMANN and CHRISTOFFEL on the non-Euclidean manifold, and which have been shaped into a system by RICCI and LEVI-CIVITA, and already applied to the problems of theoretical physics.

Relativity

Albert Einstein
Relativity Book PDF

Author : Albert Einstein
Publisher : Routledge
Page : 127 pages
File Size : 46,5 Mb
Release : 2012-08-06
Category : Philosophy
ISBN : 9781134522514

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Relativity by Albert Einstein Pdf

Time's 'Man of the Century', Albert Einstein is the unquestioned founder of modern physics. His theory of relativity is the most important scientific idea of the modern era. In this short book Einstein explains, using the minimum of mathematical terms, the basic ideas and principles of the theory which has shaped the world we live in today. Unsurpassed by any subsequent books on relativity, this remains the most popular and useful exposition of Einstein's immense contribution to human knowledge.

FUNDAMENTALS OF SPECIAL AND GENERAL RELATIVITY, Revised Edition

KRORI, K. D.
FUNDAMENTALS OF SPECIAL AND GENERAL RELATIVITY Revised Edition Book PDF

Author : KRORI, K. D.
Publisher : PHI Learning Pvt. Ltd.
Page : 332 pages
File Size : 47,7 Mb
Release : 2024-05-02
Category : Science
ISBN : 9789388028684

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FUNDAMENTALS OF SPECIAL AND GENERAL RELATIVITY, Revised Edition by KRORI, K. D. Pdf

Relativity, apart from quantum mechanics, is the greatest wonder in science, unfolded single-handedly in the 20th century by Albert Einstein. The scientist developed general relativity as a logical sequel to special relativity. This comprehensive book presents explication of the conceptual evolution and mathematical derivations of the theories of special and general relativity. The book follows an Einsteinian approach while explaining the concepts and the theories of relativity. Divided into 14 chapters, the revised edition of the book covers elementary concepts of Special relativity, as well as the advanced studies on General relativity. The recent theories like Kerr geometry, Sagnac effect, Vaidya geometry, Raychaudhuri equation and Gravitation physics vis-à-vis Quantum physics are presented in easy-to-understand language and simple style. In addition to it, the book gives an in-depth analysis on the applications of advanced theories like Vaidya-Krori-Barua solution from author’s own research works. Apart from that, the book also discusses some of the isotropic and anisotropic cosmological models, in detail. The salient topics discussed in the revised edition of the book are extrinsic curvature, detection of gravitational waves, early universe, evolution of a dead star into a white dwarf or a neutron star or a black hole, dark matter and dark energy. This book is intended for the undergraduate and postgraduate students of Physics and Mathematics. KEY FEATURES • Step-by-step derivation of equations • Easy demagogic approach • Review questions to widen the analytical understanding of the students

The Foundation of the Generalized Theory of Relativity by Albert Einstein

Albert Einstein
The Foundation of the Generalized Theory of Relativity by Albert Einstein Book PDF

Author : Albert Einstein
Publisher : Unknown
Page : 102 pages
File Size : 49,5 Mb
Release : 2020-06-14
Category : Electronic
ISBN : 9798653938153

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The Foundation of the Generalized Theory of Relativity by Albert Einstein by Albert Einstein Pdf

The theory which is sketched in the following pages forms the most wide-going generalization conceivable of what is at present known as "the theory of Relativity;" this latter theory I differentiate from the former "Special Relativity theory," and suppose it to be known. The generalization of the Relativity theory has been made much easier through the form given to the special Relativity theory by Minkowski, which mathematician was the first to recognize clearly the formal equivalence of the space like and time-like co-ordinates, and who made use of it in the building up of the theory. The mathematical apparatus useful for the general relativity theory, lay already complete in the "Absolute Differential Calculus", which were based on the researches of Gauss, Riemann and Christoffel on the non-Euclidean manifold, and which have been shaped into a system by Ricci and Levi-Civita, and already applied to the problems of theoretical physics. I have in part B of this communication developed in the simplest and clearest manner, all the supposed mathematical auxiliaries, not known to Physicists, which will be useful for our purpose, so that, a study of the mathematical literature is not necessary for an understanding of this paper. Finally in this place I thank my friend Grossmann, by whose help I was not only spared the study of the mathematical literature pertinent to this subject, but who also aided me in the researches on the field equations of gravitation.

Topics in the Foundations of General Relativity and Newtonian Gravitation Theory

David B. Malament
Topics in the Foundations of General Relativity and Newtonian Gravitation Theory Book PDF

Author : David B. Malament
Publisher : University of Chicago Press
Page : 363 pages
File Size : 47,9 Mb
Release : 2012-05-07
Category : Mathematics
ISBN : 9780226502458

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Topics in the Foundations of General Relativity and Newtonian Gravitation Theory by David B. Malament Pdf

In Topics in the Foundations of General Relativity and Newtonian Gravitation Theory, David B. Malament presents the basic logical-mathematical structure of general relativity and considers a number of special topics concerning the foundations of general relativity and its relation to Newtonian gravitation theory. These special topics include the geometrized formulation of Newtonian theory (also known as Newton-Cartan theory), the concept of rotation in general relativity, and Gödel spacetime. One of the highlights of the book is a no-go theorem that can be understood to show that there is no criterion of orbital rotation in general relativity that fully answers to our classical intuitions. Topics is intended for both students and researchers in mathematical physics and philosophy of science.

Introduction To General Relativity And Cosmology

Christian G Boehmer
Introduction To General Relativity And Cosmology Book PDF

Author : Christian G Boehmer
Publisher : World Scientific Publishing Company
Page : 287 pages
File Size : 42,5 Mb
Release : 2016-10-06
Category : Science
ISBN : 9781786341204

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Introduction To General Relativity And Cosmology by Christian G Boehmer Pdf

Introduction to General Relativity and Cosmology gives undergraduate students an overview of the fundamental ideas behind the geometric theory of gravitation and spacetime. Through pointers on how to modify and generalise Einstein's theory to enhance understanding, it provides a link between standard textbook content and current research in the field.Chapters present complicated material practically and concisely, initially dealing with the mathematical foundations of the theory of relativity, in particular differential geometry. This is followed by a discussion of the Einstein field equations and their various properties. Also given is analysis of the important Schwarzschild solutions, followed by application of general relativity to cosmology. Questions with fully worked answers are provided at the end of each chapter to aid comprehension and guide learning. This pared down textbook is specifically designed for new students looking for a workable, simple presentation of some of the key theories in modern physics and mathematics.

The Foundation of the Generalized Theory of Relativity

Albert Einstein
The Foundation of the Generalized Theory of Relativity Book PDF

Author : Albert Einstein
Publisher : Unknown
Page : 96 pages
File Size : 53,8 Mb
Release : 2020-08-16
Category : Electronic
ISBN : 1715276949

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The Foundation of the Generalized Theory of Relativity by Albert Einstein Pdf

The theory which is sketched in the following pages forms the most wide-going generalization conceivable of what is at present known as "the theory of Relativity;" this latter theory I differentiate from the former "Special Relativity theory," and suppose it to be known. The generalization of the Relativity theory has been made much easier through the form given to the special Relativity theory by Minkowski, which mathematician was the first to recognize clearly the formal equivalence of the space like and time-like co-ordinates, and who made use of it in the building up of the theory. The mathematical apparatus useful for the general relativity theory, lay already complete in the "Absolute Differential Calculus", which were based on the researches of Gauss, Riemann and Christoffel on the non-Euclidean manifold, and which have been shaped into a system by Ricci and Levi-Civita, and already applied to the problems of theoretical physics. I have in part B of this communication developed in the simplest and clearest manner, all the supposed mathematical auxiliaries, not known to Physicists, which will be useful for our purpose, so that, a study of the mathematical literature is not necessary for an understanding of this paper. Finally in this place I thank my friend Grossmann, by whose help I was not only spared the study of the mathematical literature pertinent to this subject, but who also aided me in the researches on the field equations of gravitation.

Spacetime

Marcus Kriele
Spacetime Book PDF

Author : Marcus Kriele
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 50,6 Mb
Release : 1999-10-19
Category : Mathematics
ISBN : 9783540663775

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Spacetime by Marcus Kriele Pdf

This textbook is for mathematicians and mathematical physicists and is mainly concerned with the physical justification of both the mathematical framework and the foundations of the theory of general relativity. Previous knowledge of the relevant physics is not assumed. This book is also suitable as an introduction to pseudo-Riemannian geometry with emphasis on geometrical concepts. A significant part of the text is devoted to the discussion of causality and singularity theorems. The insights obtained are applied to black hole astrophysics, thereby making the connection to current active research in mathematical physics and cosmology.

Introduction to General Relativity and Cosmology

Christian G. Böhmer
Introduction to General Relativity and Cosmology Book PDF

Author : Christian G. Böhmer
Publisher : Essential Textbooks in Physics
Page : 288 pages
File Size : 40,6 Mb
Release : 2016-10-06
Category : Cosmology
ISBN : 1786341182

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Introduction to General Relativity and Cosmology by Christian G. Böhmer Pdf

Introduction to General Relativity and Cosmology gives undergraduate students an overview of the fundamental ideas behind the geometric theory of gravitation and spacetime. Through pointers on how to modify and generalise Einstein's theory to enhance understanding, it provides a link between standard textbook content and current research in the field. Chapters present complicated material practically and concisely, initially dealing with the mathematical foundations of the theory of relativity, in particular differential geometry. This is followed by a discussion of the Einstein field equations and their various properties. Also given is analysis of the important Schwarzschild solutions, followed by application of general relativity to cosmology. Questions with fully worked answers are provided at the end of each chapter to aid comprehension and guide learning. This pared down textbook is specifically designed for new students looking for a workable, simple presentation of some of the key theories in modern physics and mathematics.

The Special Theory of Relativity

Farook Rahaman
The Special Theory of Relativity Book PDF

Author : Farook Rahaman
Publisher : Springer Nature
Page : 339 pages
File Size : 42,9 Mb
Release : 2022-04-10
Category : Science
ISBN : 9789811904974

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The Special Theory of Relativity by Farook Rahaman Pdf

This textbook expounds the major topics in the special theory of relativity. It provides a detailed examination of the mathematical foundation of the special theory of relativity, relativistic mass, relativistic mechanics, and relativistic electrodynamics. As well as covariant formulation of relativistic mechanics and electrodynamics, the text discusses the relativistic effect on photons. A new chapter on electromagnetic waves as well as several new problems and examples have been included in the second edition of the book. Using the mathematical approach, the text offers graduate students a clear, concise view of the special theory of relativity. Organized into 15 chapters and two appendices, the content is presented in a logical order, and every topic has been dealt with in a simple and lucid manner. To aid understanding of the subject, the text provides numerous relevant worked-out examples in every chapter. The mathematical approach of the text helps students in their independent study and motivates them to research the topic further.