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Author : Jose Natario
ISBN : 3642214525
Genre : Science
File Size : 68.32 MB
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“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein’s theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.

This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einstein's theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

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 : Derek F. Lawden
ISBN : 0486132145
Genre : Science
File Size : 63.72 MB
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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.

Author : James A. Foster
ISBN : 0387275835
Genre : Science
File Size : 84.53 MB
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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.

Author : James J. Callahan
ISBN : 9781475767360
Genre : Science
File Size : 40.43 MB
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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.

Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Author : Kenneth R. Lang
ISBN : 9783642359637
Genre : Science
File Size : 58.7 MB
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Essential Astrophysics is a book to learn or teach from, as well as a fundamental reference volume for anyone interested in astronomy and astrophysics. It presents astrophysics from basic principles without requiring any previous study of astronomy or astrophysics. It serves as a comprehensive introductory text, which takes the student through the field of astrophysics in lecture-sized chapters of basic physical principles applied to the cosmos. This one-semester overview will be enjoyed by undergraduate students with an interest in the physical sciences, such as astronomy, chemistry, engineering or physics, as well as by any curious student interested in learning about our celestial science. The mathematics required for understanding the text is on the level of simple algebra, for that is all that is needed to describe the fundamental principles. The text is of sufficient breadth and depth to prepare the interested student for more advanced specialised courses in the future. Astronomical examples are provided throughout the text, to reinforce the basic concepts and physics, and to demonstrate the use of the relevant formulae. In this way, the student learns to apply the fundamental equations and principles to cosmic objects and situations. Astronomical and physical constants and units as well as the most fundamental equations can be found in the appendix. Essential Astrophysics goes beyond the typical textbook by including references to the seminal papers in the field, with further reference to recent applications, results, or specialised literature.

Author : Joseph K. Cosgrove
ISBN : 9783319726311
Genre : Science
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In 1908, three years after Einstein first published his special theory of relativity, the mathematician Hermann Minkowski introduced his four-dimensional “spacetime” interpretation of the theory. Einstein initially dismissed Minkowski’s theory, remarking that “since the mathematicians have invaded the theory of relativity I do not understand it myself anymore.” Yet Minkowski’s theory soon found wide acceptance among physicists, including eventually Einstein himself, whose conversion to Minkowski’s way of thinking was engendered by the realization that he could profitably employ it for the formulation of his new theory of gravity. The validity of Minkowski’s mathematical “merging” of space and time has rarely been questioned by either physicists or philosophers since Einstein incorporated it into his theory of gravity. Physicists often employ Minkowski spacetime with little regard to the whether it provides a true account of the physical world as opposed to a useful mathematical tool in the theory of relativity. Philosophers sometimes treat the philosophy of space and time as if it were a mere appendix to Minkowski’s theory. In this critical study, Joseph Cosgrove subjects the concept of spacetime to a comprehensive examination and concludes that Einstein’s initial assessment of Minkowksi was essentially correct.

Author : Louis S. Jagerman
ISBN : 9781552125670
Genre : Science
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The Mathematics of Relativity for the Rest of Us is intended to give the generally educated reader a thorough and factual understanding of Einstein's theory of relativity - including the difficult mathematical concepts, even if the reader is not trained in higher mathematics.

The volume before us is the fourth in the series of proceedings of what used to be the Israel Colloquium for the History, Philosophy and Sociology of Science. This Colloquium has in the meantime been renamed. It now bears the name of Yehoshua Bar-Hillel (1915-1975). Bar-Hillel was an eminent philosopher of science, language, and cognition, as well as a fearless fighter for enlightenment and a passionate teacher who had a durable influence on Israeli philosophical life. The essays collected in this volume have of course this much in common, that they are all in, of, and pertaining to science. They also share the property of having all been delivered before live, and often lively, audiences in Jerusalem and in Tel Aviv, in the years 1984-1986. As is customary in the volumes of this series, the essays and commentaries presented here are intended to strike a rather special balance between the disciplines to which the Colloquium is dedicated. The historical and sociological vantage point is addressed in Kramnick's and Mali's treatment of Priestley, in Vickers' and Feldhay's studies of the Renaissance occult, and in Warnke's and Barasch's work on the imagination. From a philosophical angle several concepts, all material to the methodology of science, are taken up: rule following, by Smart and Margalit; analysis, by Ackerman; explanation, by Taylor; and the role of mathematics in physics, by Levy-Leblond and Pitowsky.

Author : Bernard F. Schutz
ISBN : 0521277035
Genre : Science
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This textbook develops general relativity and its associated mathematics from a minimum of prerequisites, leading to a physical understanding of the theory in some depth.

This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity. First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory. The goal of this book is to provide the reader with a sound conceptual understanding of both the special and general theories of relativity, and gain an insight into how the mathematics of the theory can be utilized to calculate relativistic effects.

Author : E. T. Bell
ISBN : 9780486152288
Genre : Mathematics
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Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.

Author : Piotr T. Chruściel
ISBN : 9783030284169
Genre : Mathematics
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This book provides an introduction to the mathematics and physics of general relativity, its basic physical concepts, its observational implications, and the new insights obtained into the nature of space-time and the structure of the universe. It introduces some of the most striking aspects of Einstein's theory of gravitation: black holes, gravitational waves, stellar models, and cosmology. It contains a self-contained introduction to tensor calculus and Riemannian geometry, using in parallel the language of modern differential geometry and the coordinate notation, more familiar to physicists. The author has strived to achieve mathematical rigour, with all notions given careful mathematical meaning, while trying to maintain the formalism to the minimum fit-for-purpose. Familiarity with special relativity is assumed. The overall aim is to convey some of the main physical and geometrical properties of Einstein's theory of gravitation, providing a solid entry point to further studies of the mathematics and physics of Einstein equations.

Author : I.B. Khriplovich
ISBN : 9780387274065
Genre : Science
File Size : 27.86 MB
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The book is based on the course on general relativity given regularly at the Physics Department of Novosibirsk University. The course, lasting for one semester, consists of 32 hours of lectures and 32 hours of tutorials, plus ho- work of 10 – 12 problems. The exam is passed by 30 – 35 students. The results of the homework and exam give good reasons to believe that at least 20 – 25 of these students really digest the subject. The course requires of students the knowledge of analytical mechanics and classical electrodynamics, including special relativity. Only chapters 7 and 10 of the book are in this respect exceptions: the acquaintance with the notion of spin is useful for studying chapter 7, the fundamentals of thermodynamics and quantum mechanics are necessary for the last chapter. But these parts of thebookcanbeskippedwithoutanylossforunderstandingallotherchapters. The book (as well as the course itself) is in?uenced essentially by the monographbyL.D.LandauandE.M.Lifshitz,TheClassicalTheoryofFields, (Butterworth – Heinemann, 1975). However, I strived to make the exposition as close as possible to a common university course of physics, to make it accessible not only for theorists.

This book presents the basic theory of relativity in a rational and simplest possible manner, with the emphasis on the Principle of Simplicity in developing the theory. The presentation is in the style of a discussion and is generally devoid of unproven and speculative assertions. In rare cases where speculative ideas are mentioned, they are clearly stated to be such. Test results verifying all of the theoretical results are given and discussed. This work is intended to serve as a resource and reference book for educational purposes. In Parts I and II the principal results of special and general relativity are derived rigorously, discussing the contributions of Einstein, as well as Lorentz, Poincare, Minkowski, Hilbert, Eddington and others, with historical notes touching upon the various aspects of relativity. Multiple derivations are given particularly of the mass-energy relation, the gravitational field equation, and the relativistic orbit of planets. The Schwarzschild metric and its consequences leading to the formation of black holes are treated in detail. The historical problems of physical dilation of time and Einstein's clock paradox are treated in an entirely new manner based upon general relativity. The author has also presented Einstein's gravitational radiation theory, and its application by Peters and Mathews to radiation from orbiting bodies, followed by the study of radiation from a certain binary pulsar by Weisberg and Taylor. These difficult topics are treated without taking shortcuts as is commonly done in textbooks, but in a manner that senior students can understand. A fresh look is taken of Weyl's unification of gravitational and electromagnetic field theories, again a difficult topic avoided by textbooks. The final chapter of Part II is on the elements of field cosmology. Aspects involving particle physics are not covered because they cannot be treated even cursorily in a book of this size dealing primarily with fields; only books specializing in cosmology can do justice to that vast subject. Part III is devoted entirely to tensor calculus, and its application to the geometries of Riemann and Weyl; these are the essential tools of Einstein's and Weyl's theories treated in Part II. Finally, four appendices are provided on certain mathematical topics. Thus the book is self-contained. The book contains 11 figures, an extensive bibliography and an index. Note: (1) Mathematical and other errors corrected March 21, 2015. (2) For earlier versions, a PDF of mathematical errata will be emailed upon request for free. (3) Comments of readers are welcome and may be emailed to [email protected]

Author : James Foster
ISBN : 9781475738414
Genre : Science
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Suitable as a one-semester course in general relativity for senior undergraduates or beginning graduates, this text clarifies the mathematical aspects of Einsteins general theory of relativity without sacrificing physical understanding. Beginning with an exposition of those aspects of tensor calculus and differential geometry needed for a proper exposition of the subject, the discussion turns to the space-time of general relativity and to geodesic motion, comparisons and contrasts, with Newtons theory being drawn where appropriate. A brief consideration of the field equations is followed by a discussion of physics in the vicinity of massive objects, including an elementary treatment of black holes. The book concludes with brief, introductory chapters on gravitational radiation and cosmology, and includes an appendix that reviews the special theory of relativity. In preparing this new edition, the authors have completely rewritten chapters to make the material readily accessible to physics students, while many examples, exercises and problems help guide the students through the theory.