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Tensors, Relativity and Cosmology

Tensors, Relativity and Cosmology
A Book

by Eric A. Lord

  • Publisher : Unknown Publisher
  • Release : 1976
  • Pages : 208
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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An Introduction to Tensor Calculus

An Introduction to Tensor Calculus
Relativity and Cosmology

by Derek F. Lawden

  • Publisher : Courier Corporation
  • Release : 2012-03-07
  • Pages : 224
  • ISBN : 9780486132143
  • Language : En, Es, Fr & De
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This elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult. Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory. Topics include the special principle of relativity and Lorentz transformations; orthogonal transformations and Cartesian tensors; special relativity mechanics and electrodynamics; general tensor calculus and Riemannian space; and the general theory of relativity, including a focus on black holes and gravitational waves. The text concludes with a chapter offering a sound background in applying the principles of general relativity to cosmology. Numerous exercises advance the theoretical developments of the main text, thus enhancing this volume’s appeal to students of applied mathematics and physics at both undergraduate and postgraduate levels. Preface. List of Constants. References. Bibliography.

Tensors, Relativity, and Cosmology

Tensors, Relativity, and Cosmology
A Book

by Mirjana Dalarsson,Nils Dalarsson

  • Publisher : Gulf Professional Publishing
  • Release : 2005-04-04
  • Pages : 280
  • ISBN : 9780122006814
  • Language : En, Es, Fr & De
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This book combines relativity, astrophysics, and cosmology in a single volume, providing an introduction to each subject that enables students to understand more detailed treatises as well as the current literature. The section on general relativity gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The next section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects. Lastly, the section on cosmology discusses various cosmological models, observational tests, and scenarios for the early universe. * Clearly combines relativity, astrophysics, and cosmology in a single volume so students can understand more detailed treatises and current literature * Extensive introductions to each section are followed by relevant examples and numerous exercises * Provides an easy-to-understand approach to this advanced field of mathematics and modern physics by providing highly detailed derivations of all equations and results

Tensors, Relativity, and Cosmology

Tensors, Relativity, and Cosmology
A Book

by Mirjana Dalarsson,Nils Dalarsson

  • Publisher : Academic Press
  • Release : 2015-07-08
  • Pages : 276
  • ISBN : 0128034017
  • Language : En, Es, Fr & De
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Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in motion, relativistic addition of velocities, and the twin paradox, as well as new material on gravitational waves, amongst other topics. Clearly combines relativity, astrophysics, and cosmology in a single volume Extensive introductions to each section are followed by relevant examples and numerous exercises Presents topics of interest to those researching and studying tensor calculus, the theory of relativity, gravitation, cosmology, quantum cosmology, Robertson-Walker Metrics, curvature tensors, kinematics, black holes, and more Fully revised and updated with 80 pages of new material on relativistic effects, such as relativity of simultaneity and relativity of the concept of distance, amongst other topics Provides an easy-to-understand approach to this advanced field of mathematics and modern physics by providing highly detailed derivations of all equations and results

TENSORS

TENSORS
MATHEMATICS OF DIFFERENTIAL GEOMETRY AND RELATIVITY

by AHSAN, ZAFAR

  • Publisher : PHI Learning Pvt. Ltd.
  • Release : 2015-05-21
  • Pages : 240
  • ISBN : 812035088X
  • Language : En, Es, Fr & De
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The principal aim of analysis of tensors is to investigate those relations which remain valid when we change from one coordinate system to another. This book on Tensors requires only a knowledge of elementary calculus, differential equations and classical mechanics as pre-requisites. It provides the readers with all the information about the tensors along with the derivation of all the tensorial relations/equations in a simple manner. The book also deals in detail with topics of importance to the study of special and general relativity and the geometry of differentiable manifolds with a crystal clear exposition. The concepts dealt within the book are well supported by a number of solved examples. A carefully selected set of unsolved problems is also given at the end of each chapter, and the answers and hints for the solution of these problems are given at the end of the book. The applications of tensors to the fields of differential geometry, relativity, cosmology and electromagnetism is another attraction of the present book. This book is intended to serve as text for postgraduate students of mathematics, physics and engineering. It is ideally suited for both students and teachers who are engaged in research in General Theory of Relativity and Differential Geometry.

Introduction to General Relativistic and Scalar-tensor Cosmologies

Introduction to General Relativistic and Scalar-tensor Cosmologies
A Book

by Marcelo Samuel Berman

  • Publisher : Nova Publishers
  • Release : 2007
  • Pages : 266
  • ISBN : 9781600210136
  • Language : En, Es, Fr & De
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This book offers an introduction to General Relativity and its mathematical tools, together with an introduction to relativistic and scalar-tensor cosmologies. Part I deals with Tensor Calculus. Part II introduces General Relativity Theory, while Part III deals with Relativistic Cosmology. In Part IV we work Scalar-Tensor theories, concentrating in Cosmological Models. In the last chapters, the cosmological models presented, become more and more sophisticated, including some new cases, never published elsewhere, in which all fundamental "constants" are made to vary, with the age of the Universe, namely, the gravitational, the cosmological, the coupling Brans-Dicke "constants", the speed of light, Planck's "fine -structure "constant" alpha" etc. This is a mathematical cosmology textbook that may lead undergraduates, and graduate students, to one of the frontiers of research, while keeping the prerequisites to a minimum, because most of the theory in the book requires only prior knowledge of Calculus and a University Physics course.

Cosmology in Scalar-Tensor Gravity

Cosmology in Scalar-Tensor Gravity
A Book

by Valerio Faraoni

  • Publisher : Springer Science & Business Media
  • Release : 2004-03-31
  • Pages : 274
  • ISBN : 9781402019883
  • Language : En, Es, Fr & De
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Cosmology in Scalar-Tensor Gravity covers all aspects of cosmology in scalar-tensor theories of gravity. Considerable progress has been made in this exciting area of physics and this book is the first to provide a critical overview of the research. Among the topics treated are: -Scalar-tensor gravity and its limit to general relativity, -Effective energy-momentum tensors and conformal frames, -Gravitational waves in scalar-tensor cosmology, -Specific scalar-tensor theories, -Exact cosmological solutions and cosmological perturbations, -Scalar-tensor scenarios of the early universe and inflation, -Scalar-tensor models of quintessence in the present universe and their far-reaching consequences for the ultimate fate of the cosmos.

Explorations in Mathematical Physics

Explorations in Mathematical Physics
The Concepts Behind an Elegant Language

by Don Koks

  • Publisher : Springer Science & Business Media
  • Release : 2006-09-15
  • Pages : 544
  • ISBN : 0387309438
  • Language : En, Es, Fr & De
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Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.

New Fluorinating Agents in Organic Synthesis

New Fluorinating Agents in Organic Synthesis
A Book

by Lev German,Stanislav Zemskov,L. A. Alekseeva

  • Publisher : Springer Verlag
  • Release : 1989
  • Pages : 283
  • ISBN : 9780387511603
  • Language : En, Es, Fr & De
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Relativity

Relativity
Special, General, and Cosmological

by Wolfgang Rindler

  • Publisher : Oxford University Press on Demand
  • Release : 2001
  • Pages : 428
  • ISBN : 9780198508359
  • Language : En, Es, Fr & De
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This book is a considerable amplification and modernisation of the author's earlier Essential Relativity. It aims to bring the challenge and excitement of modern relativity and cosmology at rigorous mathematical level within reach of advanced undergraduates and beginning graduates, whilecontaining enough new material to interest lecturers and researchers. Its basic purpose is to make relativity come alive conceptually. Hence the emphasis on the foundations and the logical subtleties rather than on the mathematics or the detailed experiments per se. Aided by some 300 exercises, itpromotes a visceral understanding and the confidence to tackle any fundamental relativistic problem. Following a critical overview of the whole field, special-relativistic kinematics is presented three- dimensionally before the mathematical level gradually rises. Four-vectors precede mechanics,four-tensors precede Maxwell theory, and two of the eight chapters on general relativity roll by before general tensors are needed. Three 'easy' chapters on cosmology round off the work.

General Relativity and Cosmology

General Relativity and Cosmology
A First Encounter

by Ronald J. Adler

  • Publisher : Springer Nature
  • Release : 2021-01-22
  • Pages : 313
  • ISBN : 303061574X
  • Language : En, Es, Fr & De
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Gravitational physics has now become a mainstream topic in physics and physics teaching. In particular cosmology and gravitational wave physics are at the focus of a great deal of current research. Thus it is important to introduce students to General Relativity as soon as reasonable. This textbook offers a brief but comprehensive treatment accessible to advanced undergraduate students, graduate students, and any physicist or mathematician interested in understanding the material in a short time. The author, an experienced teacher of the subject, has included numerous examples and exercises to help students consolidate the ideas they have learned.

Essential Relativity

Essential Relativity
Special, General, and Cosmological

by W. Rindler

  • Publisher : Springer
  • Release : 2013-04-17
  • Pages : 319
  • ISBN : 1475711352
  • Language : En, Es, Fr & De
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This book is an attempt to bring the full range of relativity theory within reach of advanced undergraduates, while containing enough new material and simplifications of old arguments so as not to bore the expert teacher. Roughly equal coverage is given tospecial relativity, general relativity, and cosmology. With many judicious omissions it can be taught in one semester, but it would better serve as the basis of a year's work. It is my hope, anyway, that its level and style of presentation may appeal also to wider c1asses of readers unrestricted by credit considerations. General relativity, the modern theory of gravitation in which free particles move along "straightest possible" lines in curved spacetime, and cosmology, with its dynamics for the whole possibly curved uni verse, not only seem necessary for a scientist's balanced view of the world, but offer some of the greatest intellectual thrills of modern physics. Nevertheless, considered luxuries, they are usu ally squeezed out of the graduate curriculum by the pressure of specialization. Special relativity escapes this tag with a ven geance, and tends to be taught as a pure service discipline, with too little emphasis on its startling ideas. What better time, there fore, to enjoy these subjects for their own sake than as an und- v vi PREFACE graduate? In spite of its forbidding mathematical reputation, even general relativity is accessible at that stage.

Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers

Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers
A Book

by Hung Nguyen-Schäfer,Jan-Philip Schmidt

  • Publisher : Springer
  • Release : 2016-08-16
  • Pages : 376
  • ISBN : 3662484978
  • Language : En, Es, Fr & De
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This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation • Tensor Analysis • Elementary Differential Geometry • Differential Forms • Applications of Tensors and Differential Geometry • Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.

General Relativity

General Relativity
An Introduction to Black Holes, Gravitational Waves, and Cosmology

by Michael J W Hall

  • Publisher : Morgan & Claypool Publishers
  • Release : 2018-03-23
  • Pages : 138
  • ISBN : 1681748843
  • Language : En, Es, Fr & De
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This book is based on a set of 18 class-tested lectures delivered to fourth-year physics undergraduates at Griffith University in Brisbane, and the book presents new discoveries by the Nobel-prize winning LIGO collaboration. The author begins with a review of special relativity and tensors and then develops the basic elements of general relativity (a beautiful theory that unifies special relativity and gravitation via geometry) with applications to the gravitational deflection of light, global positioning systems, black holes, gravitational waves, and cosmology. The book provides readers with a solid understanding of the underlying physical concepts; an ability to appreciate and in many cases derive important applications of the theory; and a solid grounding for those wishing to pursue their studies further. General Relativity: An Introduction to Black Holes, Gravitational Waves, and Cosmology also connects general relativity with broader topics. There is no doubt that general relativity is an active and exciting field of physics, and this book successfully transmits that excitement to readers.

An Introduction to General Relativity and Cosmology

An Introduction to General Relativity and Cosmology
A Book

by Jerzy Plebanski,Andrzej Krasinski

  • Publisher : Cambridge University Press
  • Release : 2006-08-14
  • Pages : 129
  • ISBN : 113945840X
  • Language : En, Es, Fr & De
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General relativity is a cornerstone of modern physics, and is of major importance in its applications to cosmology. Plebanski and Krasinski are experts in the field and in this book they provide a thorough introduction to general relativity, guiding the reader through complete derivations of the most important results. Providing coverage from a unique viewpoint, geometrical, physical and astrophysical properties of inhomogeneous cosmological models are all systematically and clearly presented, allowing the reader to follow and verify all derivations. For advanced undergraduates and graduates in physics and astronomy, this textbook will enable students to develop expertise in the mathematical techniques necessary to study general relativity.

General Relativity, Astrophysics, and Cosmology

General Relativity, Astrophysics, and Cosmology
A Book

by A.K. Raychaudhuri,S. Banerji,A. Banerjee

  • Publisher : Springer Science & Business Media
  • Release : 2003-11-14
  • Pages : 312
  • ISBN : 9780387406282
  • Language : En, Es, Fr & De
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For about half a century the general theory of relativity attracted little attention from physicists. However, the discovery of compact objects such as quasars and pulsars, as well as candidates for black holes on the one hand, and the microwave background radiation on the other hand completely changed the picture. In addition, developments in elementary particle physics, such as predictions of the behavior of matter at the ultrahigh energies that might have prevailed in the early stages of the big bang, have greatly en hanced the interest in general relativity. These developments created a large body of readers interested in general relativity, and its applications in astrophysics and cosmology. Having neither the time nor the inclination to delve deeply into the technical literature, such readers need a general introduction to the subject before exploring applica tions. It is for these readers that the present volume is intended. Keeping in mind the broad range of interests and wanting to avoid mathematical compli cations as much as possible, we have ventured to combine all three topics relativity, astrophysics, and cosmology-in a single volume. Naturally, we had to make a careful selection of topics to be discussed in order to keep the book to a manageable length.

Introduction To General Relativity And Cosmology

Introduction To General Relativity And Cosmology
A Book

by Christian G Boehmer

  • Publisher : World Scientific Publishing Company
  • Release : 2016-10-06
  • Pages : 288
  • ISBN : 1786341204
  • Language : En, Es, Fr & De
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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.

Proceedings of the XXIII Spanish Relativity Meeting on Reference Frames and Gravitomagnetism

Proceedings of the XXIII Spanish Relativity Meeting on Reference Frames and Gravitomagnetism
Valladolid, Spain, 6-9 September 2000

by J. F. Pascual S nchez

  • Publisher : World Scientific
  • Release : 2001-07-02
  • Pages : 380
  • ISBN : 9812810021
  • Language : En, Es, Fr & De
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This book provides an authoritative overview of the developments in gravitomagnetism which have taken place in the last few years. In particular, experiments for measuring the Lense-Thirring effect with satellites orbiting the Earth are reviewed, and an updated list of references on gravitomagnetism is included. The book also presents diverse research in general relativity and cosmology. It will be of interest to graduate students and researchers in cosmology, astrophysics, astronomy, relativity and applied mathematics. Contents: Spacetime Splitting Techniques and Gravitoelectromagnetism in General Relativity (D Bini & R T Jantzen); Black Hole Astrophysics: Gravitomagnetism and Non Keplerian Orbits (F de Felice); Gravitoelectromagnetism (B Mashhoon); Properties of Bel Currents (R Lazkoz et al.); On Cyclically Symmetrical Spacetimes (A Barnes); Scalar Field Cosmologies (J Carot & M M Collinge); Ideas Gas Stephani Universes (B Coll & J J Ferrando); Comments on Purely Electric Weyl Tensors (J J Ferrando & J A Siez); Advance of Mercury Perihelion Explained by Cogravity (C J de Matos & M Tajmar); The Intrinsic Structure of the Petrov Classification (J M Pozo & J M Parra); and other papers. Readership: Graduate students and researchers in physics, astronomy and applied mathematics."

Relativity and Cosmology

Relativity and Cosmology
Volume 5 of Modern Classical Physics

by Kip S. Thorne,Roger D. Blandford

  • Publisher : Princeton University Press
  • Release : 2021-04-13
  • Pages : 416
  • ISBN : 0691207399
  • Language : En, Es, Fr & De
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A groundbreaking textbook on twenty-first-century general relativity and cosmology Kip Thorne and Roger Blandford’s monumental Modern Classical Physics is now available in five stand-alone volumes that make ideal textbooks for individual graduate or advanced undergraduate courses on statistical physics; optics; elasticity and fluid dynamics; plasma physics; and relativity and cosmology. Each volume teaches the fundamental concepts, emphasizes modern, real-world applications, and gives students a physical and intuitive understanding of the subject. Relativity and Cosmology is an essential introduction to the subject, including remarkable recent advances. Written by award-winning physicists who have made fundamental contributions to the field and taught it for decades, the book differs from most others on the subject in important ways. It highlights recent transformations in our understanding of black holes, gravitational waves, and the cosmos; it emphasizes the physical interpretation of general relativity in terms of measurements made by observers; it explains the physics of the Riemann tensor in terms of tidal forces, differential frame dragging, and associated field lines; it presents an astrophysically oriented description of spinning black holes; it gives a detailed analysis of an incoming gravitational wave’s interaction with a detector such as LIGO; and it provides a comprehensive, in-depth account of the universe’s evolution, from its earliest moments to the present. While the book is designed to be used for a one-quarter or full-semester course, it goes deep enough to provide a foundation for understanding and participating in some areas of cutting-edge research. Includes many exercise problems Features color figures, suggestions for further reading, extensive cross-references, and a detailed index Optional “Track 2” sections make this an ideal book for a one-quarter or one-semester course An online illustration package is available to professors

A Short Course in General Relativity

A Short Course in General Relativity
A Book

by James A. Foster,J. David Nightingale

  • Publisher : Springer Science & Business Media
  • Release : 2010-04-30
  • Pages : 292
  • ISBN : 0387275835
  • Language : En, Es, Fr & De
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Suitable for a one-semester course in general relativity for senior undergraduates or beginning graduate students, this text clarifies the mathematical aspects of Einstein's theory of relativity without sacrificing physical understanding.