The Evolution Problem in General Relativity PDF Download
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Author: Sergiu Klainerman
Publisher: Springer Science & Business Media
ISBN: 146122084X
Category : Science
Languages : en
Pages : 395
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Book Description
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: Sergiu Klainerman
Publisher: Springer Science & Business Media
ISBN: 146122084X
Category : Science
Languages : en
Pages : 395
Get Book Here
Book Description
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: Einstein
Publisher: Cambridge University Press
ISBN: 9780521083713
Category : Science
Languages : en
Pages : 326
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Book Description
Author: Markus Knoflacher
Publisher: Springer Nature
ISBN: 3662694239
Category :
Languages : en
Pages : 704
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Book Description
Author: Demetrios Christodoulou
Publisher: Princeton University Press
ISBN: 1400863171
Category : Mathematics
Languages : en
Pages : 525
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Book Description
The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Denis Noble
Publisher: Cambridge University Press
ISBN: 1107176247
Category : Medical
Languages : en
Pages : 315
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Book Description
This book formulates a relativistic theory of biology, challenging the common gene-centred view of organisms.
Author: Albert Einstein
Publisher: DigiCat
ISBN:
Category : Fiction
Languages : en
Pages : 35
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Book Description
DigiCat Publishing presents to you this special edition of "Sidelights on Relativity" by Albert Einstein. DigiCat Publishing considers every written word to be a legacy of humankind. Every DigiCat book has been carefully reproduced for republishing in a new modern format. The books are available in print, as well as ebooks. DigiCat hopes you will treat this work with the acknowledgment and passion it deserves as a classic of world literature.
Author: Amitabha Ghosh
Publisher: Springer
ISBN: 9811062536
Category : Science
Languages : en
Pages : 134
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Book Description
This book provides an introduction to Newtonian and relativistic mechanics. Unlike other books on the topic, which generally take a 'top-down' approach, it follows a novel system to show how the concepts of the 'science of motion' evolved through a veritable jungle of intermediate ideas and concepts. Starting with Aristotelian philosophy, the text gradually unravels how the human mind slowly progressed towards the fundamental ideas of inertia physics. The concepts that now appear so obvious to even a high school student took great intellectuals more than a millennium to clarify. The book explores the evolution of these concepts through the history of science. After a comprehensive overview of the discovery of dynamics, it explores fundamental issues of the properties of space and time and their relation with the laws of motion. It also explores the concepts of spatio-temporal locality and fields, and offers a philosophical discussion of relative motion versus absolute motion, as well as the concept of an absolute space. Furthermore, it presents Galilean transformation and the principle of relativity, inadequacy of Galilean relativity and emergence of the spatial theory of relativity with an emphasis on physical understanding, as well as the debate over relative motion versus absolute motion and Mach's principle followed by the principle of equivalence. The natural follow-on to this section is the physical foundations of general theory of relativity. Lastly, the book ends with some new issues and possibilities regarding further modifications of the laws of motion leading to the solution of a number of fundamental issues closely connected with the characteristics of the cosmos. It is a valuable resource for undergraduate students of physics, engineering, mathematics, and related disciplines. It is also suitable for interdisciplinary coursework and introductory reading outside the classroom.
Author: Jean Eisenstaedt
Publisher: Princeton University Press
ISBN: 0691186758
Category : Science
Languages : en
Pages : 374
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Book Description
Black holes may obliterate most things that come near them, but they saved the theory of general relativity. Einstein's theory was quickly accepted as the true theory of gravity after its publication in 1915, but soon took a back seat in physics to quantum mechanics and languished for decades on the blackboards of mathematicians. Not until the existence of black holes by Stephen Hawking and Roger Penrose in the 1960s, after Einstein's death, was the theory revived. Almost one hundred years after general relativity replaced Newton's theory of gravitation, The Curious History of Relativity tells the story of both events surrounding general relativity and the techniques employed by Einstein and the relativists to construct, develop, and understand his almost impenetrable theory. Jean Eisenstaedt, one of the world's leading experts on the subject, also discusses the theory's place in the evolution of twentieth-century physics. He describes the main stages in the development of general relativity: its beginnings, its strange crossing of the desert during Einstein's lifetime while under heated criticism, and its new life from the 1960s on, when it became vital to the understanding of black holes and the observation of exotic objects, and, eventually, to the discovery of the accelerating universe. We witness Einstein's construction of his theory, as well as the work of his fascinated, discouraged, and enthusiastic colleagues--physicists, mathematicians, and astronomers. Written with flair, The Curious History of Relativity poses--and answers--the difficult questions raised by Einstein's magnificent intellectual feat.
Author: A. D'Abro
Publisher:
ISBN:
Category : Relativity (Physics).
Languages : en
Pages : 556
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Book Description
Author: Neil deGrasse Tyson
Publisher: W. W. Norton & Company
ISBN: 0393866890
Category : Science
Languages : en
Pages : 346
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Book Description
“Who can ask for better cosmic tour guides?” —Michio Kaku Our true origins are not only human, or even terrestrial, but in fact cosmic. Drawing on recent scientific breakthroughs and cross-pollination among geology, biology, astrophysics, and cosmology, Origins illuminates the soul-stirring leaps in our understanding of the cosmos. This revised and updated edition features such startling discoveries as the now more than 5,000 detected exoplanets that promise to reveal exciting possibilities for life in the cosmos, and data from a new generation of ground-based and spaceborne observatories that have fundamentally changed what we know about the expanding universe?and maybe even the laws of physics themselves. From the first image of a galaxy’s birth to tantalizing evidence of water not only on Mars but also on the asteroid Ceres, as well as on moons of Jupiter and Saturn, coauthors Neil deGrasse Tyson and Donald Goldsmith conduct an exhilarating tour of the cosmos with clarity and exuberance.
