General Relativity For Mathematicians
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General Relativity For Mathematicians
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Author : R.K. Sachs
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
General Relativity For Mathematicians written by R.K. Sachs and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is a book about physics, written for mathematicians. The readers we have in mind can be roughly described as those who: I. are mathematics graduate students with some knowledge of global differential geometry 2. have had the equivalent of freshman physics, and find popular accounts of astrophysics and cosmology interesting 3. appreciate mathematical elarity, but are willing to accept physical motiva tions for the mathematics in place of mathematical ones 4. are willing to spend time and effort mastering certain technical details, such as those in Section 1. 1. Each book disappoints so me readers. This one will disappoint: 1. physicists who want to use this book as a first course on differential geometry 2. mathematicians who think Lorentzian manifolds are wholly similar to Riemannian ones, or that, given a sufficiently good mathematical back ground, the essentials of a subject !ike cosmology can be learned without so me hard work on boring detaiis 3. those who believe vague philosophical arguments have more than historical and heuristic significance, that general relativity should somehow be "proved," or that axiomatization of this subject is useful 4. those who want an encyclopedic treatment (the books by Hawking-Ellis [1], Penrose [1], Weinberg [1], and Misner-Thorne-Wheeler [I] go further into the subject than we do; see also the survey article, Sachs-Wu [1]). 5. mathematicians who want to learn quantum physics or unified fieId theory (unfortunateIy, quantum physics texts all seem either to be for physicists, or merely concerned with formaI mathematics).
General Relativity For Mathematicians
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Author : Rainer Kurt Sachs
language : en
Publisher:
Release Date : 1977
General Relativity For Mathematicians written by Rainer Kurt Sachs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Relativity (Physics) categories.
The General Theory Of Relativity
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Author : Anadijiban Das
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-26
The General Theory Of Relativity written by Anadijiban Das and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-26 with Science categories.
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.
General Relativity And The Einstein Equations
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Author : Yvonne Choquet-Bruhat
language : en
Publisher: Oxford University Press
Release Date : 2009
General Relativity And The Einstein Equations written by Yvonne Choquet-Bruhat and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.
Supersymmetry For Mathematicians An Introduction
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Author : V. S. Varadarajan
language : en
Publisher: American Mathematical Soc.
Release Date :
Supersymmetry For Mathematicians An Introduction written by V. S. Varadarajan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
An special feature of the book is the treatment in depth of the theory of spinors in all dimensions and signatures, which is the basis of all developments of supergeometry both in physics and mathematics, especially in quantum field theory and supergravity."--Jacket.
Mathematical Problems Of General Relativity I
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Author : Demetrios Christodoulou
language : en
Publisher: European Mathematical Society
Release Date : 2008
Mathematical Problems Of General Relativity I written by Demetrios Christodoulou and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
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.
A Mathematical Introduction To General Relativity
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Author : Amol Sasane
language : en
Publisher: World Scientific
Release Date : 2021-08-10
A Mathematical Introduction To General Relativity written by Amol Sasane and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-10 with Science categories.
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.
General Relativity For Mathematicians
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Author : Rainer K. Sachs
language : en
Publisher:
Release Date : 1977
General Relativity For Mathematicians written by Rainer K. Sachs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
Spacetime
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Author : Marcus Kriele
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-10-19
Spacetime written by Marcus Kriele and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-19 with Mathematics categories.
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.
Mathematical Theory Of General Relativity
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Author : L. N. Katkar
language : en
Publisher:
Release Date : 2014
Mathematical Theory Of General Relativity written by L. N. Katkar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Science categories.
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.