AN ESSAY ON THE MATHEMATICAL METHODS OF THEORY OF GENERAL RELATIVITY PDF Download
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Author: Edoardo Confalonieri
Publisher: Edoardo Confalonieri
ISBN:
Category :
Languages : en
Pages : 2233
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Book Description
The basic concepts of a method for a general integral of the Field Equations of the Theory of General Relativity are outlined. An extended and revised version is currently in preparation, and it will be uploaded as soon as ready for publication.
Author: Edoardo Confalonieri
Publisher: Edoardo Confalonieri
ISBN:
Category :
Languages : en
Pages : 2233
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Book Description
The basic concepts of a method for a general integral of the Field Equations of the Theory of General Relativity are outlined. An extended and revised version is currently in preparation, and it will be uploaded as soon as ready for publication.
Author: Amol Sasane
Publisher: World Scientific
ISBN: 9811243794
Category : Science
Languages : en
Pages : 500
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Book Description
The book aims to give a mathematical presentation of the theory of general relativity (that is, spacetime-geometry-based gravitation theory) to advanced undergraduate mathematics students. Mathematicians will find spacetime physics presented in the definition-theorem-proof format familiar to them. The given precise mathematical definitions of physical notions help avoiding pitfalls, especially in the context of spacetime physics describing phenomena that are counter-intuitive to everyday experiences.In the first part, the differential geometry of smooth manifolds, which is needed to present the spacetime-based gravitation theory, is developed from scratch. Here, many of the illustrating examples are the Lorentzian manifolds which later serve as spacetime models. This has the twofold purpose of making the physics forthcoming in the second part relatable, and the mathematics learnt in the first part less dry. The book uses the modern coordinate-free language of semi-Riemannian geometry. Nevertheless, to familiarise the reader with the useful tool of coordinates for computations, and to bridge the gap with the physics literature, the link to coordinates is made through exercises, and via frequent remarks on how the two languages are related.In the second part, the focus is on physics, covering essential material of the 20th century spacetime-based view of gravity: energy-momentum tensor field of matter, field equation, spacetime examples, Newtonian approximation, geodesics, tests of the theory, black holes, and cosmological models of the universe.Prior knowledge of differential geometry or physics is not assumed. The book is intended for self-study, and the solutions to the (over 200) exercises are included.
Author: Demetrios Christodoulou
Publisher: European Mathematical Society
ISBN: 9783037190050
Category : Science
Languages : en
Pages : 164
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Book Description
General relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newton's theory of gravitation as well as Newton's equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of Gauss' intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler-Lagrange system of partial differential equations. Another method, the study and systematic use of foliations by characteristic (null) hypersurfaces, is in the spirit of Roger Penrose's approach in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media. The book is intended for advanced students and researchers seeking an introduction to the methods and applications of general relativity.
Author: L. N. Katkar
Publisher:
ISBN: 9781842658062
Category : Science
Languages : en
Pages : 0
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Book Description
Explores the laws of general relativity. The contents of the book will attract both mathematicians and physicists which provides motivation and applications of many ideas and powerful mathematical methods of modern analysis and differential geometry.
Author: Allen I. Janis
Publisher: Springer Science & Business Media
ISBN: 9780817635411
Category : Science
Languages : en
Pages : 282
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Book Description
Papers from the Discussion Conference on Recent Advances in General Relativity, held at the U. of Pittsburgh, May 1990, survey the interacting fields of classical general relativity, astrophysics, and quantum gravity. Some of the remarks made following the invited papers are also included. The conference also included three workshops on classical g
Author: James Malcolm Bird
Publisher:
ISBN:
Category : Gravitation
Languages : en
Pages : 382
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Book Description
Einstein's theory of relativity confounded and excited both professional and amateur scientists with its explanation of the intricacies of how the world and the universe truly work, rather than how people wished or believed they worked. His view of relativity dismantled Newton's theory of space and time as absolutes, adding the concept of curved space-time, which deals with the velocity of motion. Einstein explains his theory of physics in a way that was designed not only for scientists with a knowledge of the complicated math involved but for the general reader as well.
Author: Albert Einstein
Publisher: Diamond Pocket Books Pvt Ltd
ISBN: 9390960711
Category : Biography & Autobiography
Languages : en
Pages : 188
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Book Description
Albert Einstein, a Nobel laureate, has changed the world with his research and theories. He is regarded as the founder of modern physics. Besides ‘Relativity’, he worked on Photoelectric effect, Brownian motion, Special relativity, and Mass-Energy equivalence (E=mc2). They reformed the views on time, space and matter. Allert Einstein developed the general theory of ‘Relativity’. He published ‘Relativity: The Special and the General Theory’ in German. Its first English translation was published in 1920. The book deals with the special theory of relativity, the general theory of relativity, and the considerations on the universe as a whole The book gives an exact insight into the theory of Relativity. It covers, the system of Co-ordinates; The Lorentz Transformation; The experiment of Fizeau; Minkowski’s four dimensional space; The Gravitational Field; Gaussian Co-ordinates; The structure of space, and lot many other scientific concepts thus will be highly beneficial to the Readers. A must have book for everyone related to modern physics.
Author: Antonio Romano
Publisher: Springer Nature
ISBN: 3030272370
Category : Science
Languages : en
Pages : 496
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Book Description
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: Anadijiban Das
Publisher: Springer Science & Business Media
ISBN: 1461436583
Category : Science
Languages : en
Pages : 694
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Book Description
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: Frank J. Tipler
Publisher: Academic Press
ISBN: 1483273628
Category : Science
Languages : en
Pages : 255
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Book Description
Essays in General Relativity: A Festschrift for Abraham Taub is collection of essays to honor Professor Abraham H. Taub on the occasion of his retirement from the mathematics faculty of the University of California at Berkeley. Relativistic hydrodynamics has always been a subject dear to Taub's heart. In fact, many basic results on special relativistic fluid flows are due to him, and he has been a major contributor to the study of fluid flows near shocks. The book contains 16 chapters and begins with a discussion of a geometrical approach to general relativity. This is followed by separate chapters that examine the topology of the space-time manifold representing a stellar model; the notion of an ""external return"" in the context of general relativity; and the standard two-surface integral formulation of gravitational energy and momentum. Subsequent chapters deal with tidal forces in a highly asymmetric Taub universe; derivation of theoretical upper limits on the strengths of the gravitational waves that bathe the Earth; and a new formulation of Lagrangian general relativistic hydrodynamics.
