The Cauchy Problem in General Relativity

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Publisher : European Mathematical Society
ISBN 13 : 9783037190531
Total Pages : 310 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis The Cauchy Problem in General Relativity by : Hans Ringström

Download or read book The Cauchy Problem in General Relativity written by Hans Ringström and published by European Mathematical Society. This book was released on 2009 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theory of relativity is a theory of manifolds equipped with Lorentz metrics and fields which describe the matter content. Einstein's equations equate the Einstein tensor (a curvature quantity associated with the Lorentz metric) with the stress energy tensor (an object constructed using the matter fields). In addition, there are equations describing the evolution of the matter. Using symmetry as a guiding principle, one is naturally led to the Schwarzschild and Friedmann-Lemaitre-Robertson-Walker solutions, modelling an isolated system and the entire universe respectively. In a different approach, formulating Einstein's equations as an initial value problem allows a closer study of their solutions. This book first provides a definition of the concept of initial data and a proof of the correspondence between initial data and development. It turns out that some initial data allow non-isometric maximal developments, complicating the uniqueness issue. The second half of the book is concerned with this and related problems, such as strong cosmic censorship. The book presents complete proofs of several classical results that play a central role in mathematical relativity but are not easily accessible to those without prior background in the subject. Prerequisites are a good knowledge of basic measure and integration theory as well as the fundamentals of Lorentz geometry. The necessary background from the theory of partial differential equations and Lorentz geometry is included.

Studies in the History of General Relativity

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Publisher : Springer Science & Business Media
ISBN 13 : 9780817634797
Total Pages : 488 pages
Book Rating : 4.6/5 (347 download)

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Book Synopsis Studies in the History of General Relativity by : Jean Eisenstaedt

Download or read book Studies in the History of General Relativity written by Jean Eisenstaedt and published by Springer Science & Business Media. This book was released on 1992-02-07 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the considerations of the two dozen papers are the reception and development of Einstein's theory of general relativity in various institutions around the world; conceptual issues of the theory, especially themes, concepts, and principles associated with his theory of gravity; a number of tech

The Einstein Equations and the Large Scale Behavior of Gravitational Fields

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Publisher : Birkhäuser
ISBN 13 : 3034879539
Total Pages : 487 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Einstein Equations and the Large Scale Behavior of Gravitational Fields by : Piotr T. Chrusciel

Download or read book The Einstein Equations and the Large Scale Behavior of Gravitational Fields written by Piotr T. Chrusciel and published by Birkhäuser. This book was released on 2012-12-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.

CAUCHY PROBLEM IN GENERAL RELATIVITY.

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Publisher :
ISBN 13 : 9783037195536
Total Pages : pages
Book Rating : 4.1/5 (955 download)

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Book Synopsis CAUCHY PROBLEM IN GENERAL RELATIVITY. by : HANS RINGSTROM.

Download or read book CAUCHY PROBLEM IN GENERAL RELATIVITY. written by HANS RINGSTROM. and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Large Scale Structure of Space-Time

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Publisher : Cambridge University Press
ISBN 13 : 1139810952
Total Pages : 406 pages
Book Rating : 4.1/5 (398 download)

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Book Synopsis The Large Scale Structure of Space-Time by : S. W. Hawking

Download or read book The Large Scale Structure of Space-Time written by S. W. Hawking and published by Cambridge University Press. This book was released on 1975-02-27 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.

Unsolved Problems in Special and General Relativity

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Publisher : Infinite Study
ISBN 13 : 1599732203
Total Pages : 319 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Unsolved Problems in Special and General Relativity by : Florentin Smarandache

Download or read book Unsolved Problems in Special and General Relativity written by Florentin Smarandache and published by Infinite Study. This book was released on 2013 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt:

3+1 Formalism in General Relativity

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Publisher : Springer
ISBN 13 : 3642245250
Total Pages : 294 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis 3+1 Formalism in General Relativity by : Éric Gourgoulhon

Download or read book 3+1 Formalism in General Relativity written by Éric Gourgoulhon and published by Springer. This book was released on 2012-02-27 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.

Introduction to General Relativity, Black Holes, and Cosmology

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Publisher : Oxford University Press, USA
ISBN 13 : 0199666466
Total Pages : 301 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Introduction to General Relativity, Black Holes, and Cosmology by : Yvonne Choquet-Bruhat

Download or read book Introduction to General Relativity, Black Holes, and Cosmology written by Yvonne Choquet-Bruhat and published by Oxford University Press, USA. This book was released on 2015 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics. Based on Yvonne Choquet-Bruhat's more advanced text, General Relativity and the Einstein Equations, the aim of this book is to give with precision, but as simply as possible, the foundations and main consequences of General Relativity. The first five chapters from General Relativity and the Einstein Equations have been updated with new sections and chapters on black holes, gravitational waves, singularities, and the Reissner-Nordstrom and interior Schwarzchild solutions. The rigour behind this book will provide readers with the perfect preparation to follow the great mathematical progress in the actual development, as well as the ability to model, the latest astrophysical and cosmological observations. The book presents basic General Relativity and provides a basis for understanding and using the fundamental theory.

Conformal Methods in General Relativity

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Publisher : Cambridge University Press
ISBN 13 : 1009291343
Total Pages : 627 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis Conformal Methods in General Relativity by : Juan A. Valiente Kroon

Download or read book Conformal Methods in General Relativity written by Juan A. Valiente Kroon and published by Cambridge University Press. This book was released on 2023-01-31 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2016 volume, now reissued as OA, shows how conformal methods can be used to study Einstein's theory of gravity.

Einstein’s Field Equations and Their Physical Implications

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Publisher : Springer
ISBN 13 : 3540465804
Total Pages : 433 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Einstein’s Field Equations and Their Physical Implications by : Bernd G. Schmidt

Download or read book Einstein’s Field Equations and Their Physical Implications written by Bernd G. Schmidt and published by Springer. This book was released on 2008-01-11 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves two purposes. The authors present important aspects of modern research on the mathematical structure of Einstein's field equations and they show how to extract their physical content from them by mathematically exact methods. The essays are devoted to exact solutions and to the Cauchy problem of the field equations as well as to post-Newtonian approximations that have direct physical implications. Further topics concern quantum gravity and optics in gravitational fields. The book addresses researchers in relativity and differential geometry but can also be used as additional reading material for graduate students.

The Evolution Problem in General Relativity

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Publisher : Springer Science & Business Media
ISBN 13 : 146122084X
Total Pages : 395 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Evolution Problem in General Relativity by : Sergiu Klainerman

Download or read book The Evolution Problem in General Relativity written by Sergiu Klainerman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this work is to revisit the proof of the global stability of Minkowski space by D. Christodoulou and S. Klainerman, [Ch-KI]. We provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets. This can also be interpreted as a proof of the global stability of the external region of Schwarzschild spacetime. The proof, which is a significant modification of the arguments in [Ch-Kl], is based on a double null foliation of spacetime instead of the mixed null-maximal foliation used in [Ch-Kl]. This approach is more naturally adapted to the radiation features of the Einstein equations and leads to important technical simplifications. In the first chapter we review some basic notions of differential geometry that are sys tematically used in all the remaining chapters. We then introduce the Einstein equations and the initial data sets and discuss some of the basic features of the initial value problem in general relativity. We shall review, without proofs, well-established results concerning local and global existence and uniqueness and formulate our main result. The second chapter provides the technical motivation for the proof of our main theorem.

An Introduction to Mathematical Relativity

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Publisher : Springer Nature
ISBN 13 : 3030656837
Total Pages : 186 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis An Introduction to Mathematical Relativity by : José Natário

Download or read book An Introduction to Mathematical Relativity written by José Natário and published by Springer Nature. This book was released on 2021-03-24 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise textbook introduces the reader to advanced mathematical aspects of general relativity, covering topics like Penrose diagrams, causality theory, singularity theorems, the Cauchy problem for the Einstein equations, the positive mass theorem, and the laws of black hole thermodynamics. It emerged from lecture notes originally conceived for a one-semester course in Mathematical Relativity which has been taught at the Instituto Superior Técnico (University of Lisbon, Portugal) since 2010 to Masters and Doctorate students in Mathematics and Physics. Mostly self-contained, and mathematically rigorous, this book can be appealing to graduate students in Mathematics or Physics seeking specialization in general relativity, geometry or partial differential equations. Prerequisites include proficiency in differential geometry and the basic principles of relativity. Readers who are familiar with special relativity and have taken a course either in Riemannian geometry (for students of Mathematics) or in general relativity (for those in Physics) can benefit from this book.

On the Topology and Future Stability of the Universe

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Publisher : OUP Oxford
ISBN 13 : 0199680299
Total Pages : 733 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis On the Topology and Future Stability of the Universe by : Hans Ringström

Download or read book On the Topology and Future Stability of the Universe written by Hans Ringström and published by OUP Oxford. This book was released on 2013-05-23 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general introduction to the initial value problem for Einstein's equations coupled to collisionless matter. The book contains a proof of future stability of models of the universe consistent with the current observational data and a discussion of the restrictions on the possible shapes of the universe imposed by observations.

Partial Differential Equations in General Relativity

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Publisher :
ISBN 13 :
Total Pages : 304 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Partial Differential Equations in General Relativity by : Alan D. Rendall

Download or read book Partial Differential Equations in General Relativity written by Alan D. Rendall and published by . This book was released on 2008-04-03 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text that will bring together PDE theory, general relativity and astrophysics to deliver an overview of theory of partial differential equations for general relativity. The text will include numerous examples and provide a unique resource for graduate students in mathematics and physics, numerical relativity and cosmology.

General Relativity and the Einstein Equations

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Publisher : Oxford University Press
ISBN 13 : 0199230722
Total Pages : 812 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis General Relativity and the Einstein Equations by : Yvonne Choquet-Bruhat

Download or read book General Relativity and the Einstein Equations written by Yvonne Choquet-Bruhat and published by Oxford University Press. This book was released on 2009 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

General Relativity and Gravitation

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Publisher : Cambridge University Press
ISBN 13 : 1316298698
Total Pages : 697 pages
Book Rating : 4.3/5 (162 download)

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Book Synopsis General Relativity and Gravitation by : Abhay Ashtekar

Download or read book General Relativity and Gravitation written by Abhay Ashtekar and published by Cambridge University Press. This book was released on 2015-06-01 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore spectacular advances in cosmology, relativistic astrophysics, gravitational wave science, mathematics, computational science, and the interface of gravitation and quantum physics with this unique celebration of the centennial of Einstein's discovery of general relativity. Twelve comprehensive and in-depth reviews, written by a team of world-leading international experts, together present an up-to-date overview of key topics at the frontiers of these areas, with particular emphasis on the significant developments of the last three decades. Interconnections with other fields of research are also highlighted, making this an invaluable resource for both new and experienced researchers. Commissioned by the International Society on General Relativity and Gravitation, and including accessible introductions to cutting-edge topics, ample references to original research papers, and informative colour figures, this is a definitive reference for researchers and graduate students in cosmology, relativity, and gravitational science.

Einstein Spaces

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Publisher : Elsevier
ISBN 13 : 1483151840
Total Pages : 426 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Einstein Spaces by : A. Z. Petrov

Download or read book Einstein Spaces written by A. Z. Petrov and published by Elsevier. This book was released on 2016-08-19 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Einstein Spaces presents the mathematical basis of the theory of gravitation and discusses the various spaces that form the basis of the theory of relativity. This book examines the contemporary development of the theory of relativity, leading to the study of such problems as gravitational radiation, the interaction of fields, and the behavior of elementary particles in a gravitational field. Organized into nine chapters, this book starts with an overview of the principles of the special theory of relativity, with emphasis on the mathematical aspects. This text then discusses the need for a general classification of all potential gravitational fields, and in particular, Einstein spaces. Other chapters consider the gravitational fields in empty space, such as in a region where the energy-momentum tensor is zero. The final chapter deals with the problem of the limiting conditions in integrating the gravitational field equations. Physicists and mathematicians will find this book useful.