Mathematical Problems Of General Relativity I
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Author | : Demetrios Christodoulou |
Publisher | : European Mathematical Society |
Total Pages | : 164 |
Release | : 2008 |
Genre | : Science |
ISBN | : 9783037190050 |
Download Mathematical Problems of General Relativity I Book in PDF, Epub and Kindle
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 | : DEMETRIOS CHRISTODOULOU. |
Publisher | : |
Total Pages | : |
Release | : |
Genre | : |
ISBN | : 9783037195055 |
Download MATHEMATICAL PROBLEMS OF GENERAL RELATIVITY I. Book in PDF, Epub and Kindle
Author | : Florentin Smarandache |
Publisher | : Infinite Study |
Total Pages | : 319 |
Release | : 2013 |
Genre | : Relativity (Physics) |
ISBN | : 1599732203 |
Download Unsolved Problems in Special and General Relativity Book in PDF, Epub and Kindle
Author | : Dēmētrēs Ch Christodulu |
Publisher | : |
Total Pages | : 0 |
Release | : 20?? |
Genre | : |
ISBN | : |
Download Mathematical Problems of General Relativity Book in PDF, Epub and Kindle
Author | : Hans Ringström |
Publisher | : European Mathematical Society |
Total Pages | : 310 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 9783037190531 |
Download The Cauchy Problem in General Relativity Book in PDF, Epub and Kindle
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.
Author | : Sergiu Klainerman |
Publisher | : Springer Science & Business Media |
Total Pages | : 395 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 146122084X |
Download The Evolution Problem in General Relativity Book in PDF, Epub and Kindle
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.
Author | : L. P. Hughston |
Publisher | : Cambridge University Press |
Total Pages | : 196 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 9780521339438 |
Download An Introduction to General Relativity Book in PDF, Epub and Kindle
This textbook provides an introduction to general relativity for mathematics undergraduates or graduate physicists. After a review of Cartesian tensor notation and special relativity the concepts of Riemannian differential geometry are introducted. More emphasis is placed on an intuitive grasp of the subject and a calculational facility than on a rigorous mathematical exposition. General relativity is then presented as a relativistic theory of gravity reducing in the appropriate limits to Newtonian gravity or special relativity. The Schwarzchild solution is derived and the gravitational red-shift, time dilation and classic tests of general relativity are discussed. There is a brief account of gravitational collapse and black holes based on the extended Schwarzchild solution. Other vacuum solutions are described, motivated by their counterparts in linearised general relativity. The book ends with chapters on cosmological solutions to the field equations. There are exercises attached to each chapter, some of which extend the development given in the text.
Author | : N.M.J. Woodhouse |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2007-03-06 |
Genre | : Science |
ISBN | : 1846284872 |
Download General Relativity Book in PDF, Epub and Kindle
Based on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study.
Author | : Yvonne Choquet-Bruhat |
Publisher | : Oxford University Press |
Total Pages | : 812 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0199230722 |
Download General Relativity and the Einstein Equations Book in PDF, Epub and Kindle
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.
Author | : Piotr T. Chrusciel |
Publisher | : Birkhäuser |
Total Pages | : 487 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3034879539 |
Download The Einstein Equations and the Large Scale Behavior of Gravitational Fields Book in PDF, Epub and Kindle
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.