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Author : Farook Rahaman
Publisher : Cambridge University Press
Page : 427 pages
File Size : 48,7 Mb
Release : 2021-09-30
Category : Science
ISBN : 9781108837996
Discusses the general theory of relativity, Lie derivatives, rotating black holes, with a focus on basics of cosmology and astrophysics.
Author : Ahmad Shariati
Publisher : Elsevier
Page : 352 pages
File Size : 53,8 Mb
Release : 2022-09-09
Category : Mathematics
ISBN : 9780323997096
A Mathematical Approach to Special Relativity introduces the mathematical formalisms of special and general relativity. Developed from the author’s experience teaching physics to students across all levels, the valuable resource introduces key concepts, building in complexity and using increasingly advanced mathematical tools as it progresses. Without assuming a background in calculus, the text begins with symmetry, before delving more deeply into Galilean relativity. Throughout, the book provides examples and useful "Guides to the Literature." This unique text emphasizes the experimental consequences and verifications of the underpinning theory in order to provide students with a solid foundation in this key area. Based on the professor’s 25+ years of experience teaching physics students at every level Covers key topics in special relativity, including some group theory, as well as an introduction to general relativity and basic differential geometry Contains numerous worked examples and "Guides to the Literature" throughout the text
Author : Farook Rahaman
Publisher : Springer Nature
Page : 339 pages
File Size : 55,8 Mb
Release : 2022-04-10
Category : Science
ISBN : 9789811904974
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.
Author : Antonio Romano,Mario Mango Furnari
Publisher : Springer Nature
Page : 496 pages
File Size : 42,5 Mb
Release : 2019-09-25
Category : Science
ISBN : 9783030272371
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.
Author : George Trimble
Publisher : Unknown
Page : 160 pages
File Size : 53,8 Mb
Release : 2015-06-20
Category : Electronic
ISBN : 1514285630
RelativitySimple, Shocking, WorthwhileThe mathematics is SIMPLE. Only high school algebra is used. It is the concepts that are difficult to grasp because they require you to set aside commonly held notions about reality and accept truths that are profoundly counterintuitive. Special Relativity is shocking. From simple premises come mind-bending corollaries that excite the imagination. Ideas like time travel, length contraction, time dilation, and the twin paradox are all easily understood with an understanding of Einstein's great theorem.While conceptually challenging, it is worth the effort! Dr. Trimble will make Einstein's theory of special relativity entertaining, engaging and attainable. Plan for some enjoyable afternoons of fun and learning.
Author : N.M.J. Woodhouse
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447100836
This book provides readers with the tools needed to understand the physical basis of special relativity and will enable a confident mathematical understanding of Minkowski's picture of space-time. It features a large number of examples and exercises, ranging from the rather simple through to the more involved and challenging. Coverage includes acceleration and tensors and has an emphasis on space-time diagrams.
Author : Peter Lorimer
Publisher : World Scientific
Page : 116 pages
File Size : 46,9 Mb
Release : 1990-07-05
Category : Science
ISBN : 9789814506861
One of the problems facing mathematics and physics is that mathematicians and physicists speak languages that the others find hard to understand. These notes take a fundamental part of physics, the special theory of relativity and describe it in terms that can be understood by mathematics students who have studied the two basic undergraduate topics, linear algebra and multivariable calculus. It gives a full description of the geometry of space-time and the foundations of the theory of electromagnetism in terms they are familiar with.
Author : Tevian Dray
Publisher : CRC Press
Page : 151 pages
File Size : 44,6 Mb
Release : 2012-07-02
Category : Mathematics
ISBN : 9781466510470
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.
Author : Michael Tsamparlis
Publisher : Springer Science & Business Media
Page : 605 pages
File Size : 41,7 Mb
Release : 2010-05-17
Category : Science
ISBN : 9783642038372
Writing a new book on the classic subject of Special Relativity, on which numerous important physicists have contributed and many books have already been written, can be like adding another epicycle to the Ptolemaic cosmology. Furthermore, it is our belief that if a book has no new elements, but simply repeats what is written in the existing literature, perhaps with a different style, then this is not enough to justify its publication. However, after having spent a number of years, both in class and research with relativity, I have come to the conclusion that there exists a place for a new book. Since it appears that somewhere along the way, mathem- ics may have obscured and prevailed to the degree that we tend to teach relativity (and I believe, theoretical physics) simply using “heavier” mathematics without the inspiration and the mastery of the classic physicists of the last century. Moreover current trends encourage the application of techniques in producing quick results and not tedious conceptual approaches resulting in long-lasting reasoning. On the other hand, physics cannot be done a ́ la carte stripped from philosophy, or, to put it in a simple but dramatic context A building is not an accumulation of stones! As a result of the above, a major aim in the writing of this book has been the distinction between the mathematics of Minkowski space and the physics of r- ativity.
Author : Wladimir-Georges Boskoff,Salvatore Capozziello
Publisher : Springer Nature
Page : 412 pages
File Size : 44,6 Mb
Release : 2020-06-01
Category : Science
ISBN : 9783030478940
This book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.
Author : Arthur Stanley Eddington
Publisher : Mjp Publishers
Page : 0 pages
File Size : 46,6 Mb
Release : 2023-02-15
Category : Fiction
ISBN : 9355280025
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author : Helmut Günther
Publisher : Springer Nature
Page : 350 pages
File Size : 52,9 Mb
Release : 2020-05-16
Category : Science
ISBN : 9789811531682
This book presents an alternative representation of Einstein's Special Theory of Relativity, which makes Special Relativity much more comprehensible. Moreover, one will come across a fundamental relationship between the Special Theory of Relativity and the mechanics of space lattice. In all previous formulations, the Einsteinian special principle of relativity, in one or the other form is used as the starting point for Special Relativity. In correspondence to this principle, one takes it as granted apriori, that all observers independent of their uniform motion to each other measure one and the same propagation velocity of a light signal. This book is thought of as a lecture for physicists, mathematicians and computer scientists and concentrates on the students of these fields. The book should reach a broad circle of interested readers from the fields of natural sciences and philosophy and provide and invigorating experience for engineers.
Author : Anadijiban Das,Andrew DeBenedictis
Publisher : Springer Science & Business Media
Page : 694 pages
File Size : 42,6 Mb
Release : 2012-06-26
Category : Science
ISBN : 9781461436584
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.
Author : Thomas Strohm
Publisher : Springer Nature
Page : 347 pages
File Size : 54,9 Mb
Release : 2023-04-17
Category : Science
ISBN : 9783031219245
This textbook introduces special relativity with a focus on a profound understanding of the physics behind the theory. The main part of the book is targeted to undergraduates, for physics education, for undergraduate students in natural sciences in general, and even to interested laypersons. To serve these target groups, the book uses only basic mathematics and, in contrast to many other introductions to special relativity, the book is based on a pedagogical approach that relies on geometry and space-time diagrams to make the surprising predictions of the theory particularly clear. Special relativity is a geometric theory, and space-time diagrams are an efficient and easily understandable way to comprehend its implications. The textbook, however, is also suitable for advanced students and enthusiasts that already learned the basics of the special theory of relativity and want to know more. Special digression sections provide plenty of interesting material. Carefully selected problems with solutions and in-depth explanations for all key experiments help deepen the knowledge.
Author : KRORI, K. D.
Publisher : PHI Learning Pvt. Ltd.
Page : 332 pages
File Size : 46,9 Mb
Release : 2024-07-03
Category : Science
ISBN : 9789388028684
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