Download or read book Stability by Linearization of Einstein s Field Equation written by Lluís Bruna and published by Springer Science & Business Media. This book was released on 2013-11-25 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: V ? V ?K? , 3 2 2 R ? /?x K i i g V T G g ?T , ? G g g 4 ? R ? ? G ? T g g ? h h ? 2 2 2 2 ? ? ? ? ? ? ? h ?S , ?? ?? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 S T S T? T?. ? ̃ T S 2 2 2 2 ? ? ? ? ? ? ? h . ?? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 g h h ?? g T T g vacuum M n R n R Acknowledgements n R Chapter I Pseudo-Riemannian Manifolds I.1 Connections M C n X M C M F M C X M F M connection covariant derivative M ? X M ×X M ?? X M X,Y ?? Y X ? Y ? Y ? Y X +X X X 1 2 1 2 ? Y Y ? Y ? Y X 1 2 X 1 X 2 ? Y f? Y f?F M fX X ? fY X f Y f? Y f?F M X X ? torsion ? Y?? X X,Y X,Y?X M . X Y localization principle Theorem I.1. Let X, Y, X , Y be C vector ?elds on M.Let U be an open set

Download or read book How Einstein Found His Field Equations written by Michel Janssen and published by Springer Nature. This book was released on 2022-07-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Einstein's field equations of gravitation are a core element of his general theory of relativity. In four short communications to the Prussian Academy of Sciences in Berlin in November 1015, we can follow the final steps toward these equations and the resulting theory's spectacular success in accounting for the anomalous motion of Mercury's perihelion. This source book provides an expert guide to these four groundbreaking papers. Following an introductory essay placing these papers in the context of the development of Einstein's theory, it presents and analyzes, in addition to the four papers of November 1915, a careful selection of (critical excerpts from) papers, letters, and manuscripts documenting the path that early on led Einstein to the field equations of the first November 1915 paper, but then took a turn away from them only to lead back to them in the end. Drawing on extensive research at the Einstein Papers Project and the Max Planck Institute for History of Science, this volume traces the intricate interplay between considerations of physics and considerations of mathematics that guided Einstein along this path. It thus presents a concise yet authoritative account of how Einstein found his field equations, affording readers who are prepared to immerse themselves in these intricacies a unique glimpse of Einstein at work at the height of his creative prowess. Highlights of this journey in Einstein's footsteps include the crucial pages (with detailed annotation) from the Zurich Notebook, the record of Einstein's early search for field equation with his mathematician friend Marcel Grossmann, and the Einstein-Besso manuscript, documenting Einstein's attempts with his friend and confidant Michele Besso to explain the Mercury anomaly on the basis of the equations that he and Grossmann had eventually settled on in the Zurich Notebook.

Download or read book Semiclassical and Stochastic Gravity written by Bei-Lok B. Hu and published by Cambridge University Press. This book was released on 2020-03-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of semi-classical gravity theory and stochastic gravity as theories of quantum gravity in curved space-time.

Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1975-02 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book General Relativity and Gravitation written by M. A. H. MacCallum and published by CUP Archive. This book was released on 1987-09-24 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book General Relativity written by Robert M. Wald and published by University of Chicago Press. This book was released on 2010-05-15 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Wald's book is clearly the first textbook on general relativity with a totally modern point of view; and it succeeds very well where others are only partially successful. The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement "Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today

Download or read book New Directions in Applied Mathematics written by P.J. Hilton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is close enough to the end of the century to make a guess as to what the Encyclopedia Britannica article on the history of mathematics will report in 2582: "We have said that the dominating theme of the Nineteenth Century was the development and application of the theory of functions of one variable. At the beginning of the Twentieth Century, mathematicians turned optimistically to the study off unctions of several variables. But wholly unexpected difficulties were met, new phenomena were discovered, and new fields of mathematics sprung up to study and master them. As a result, except where development of methods from earlier centuries continued, there was a recoil from applications. Most of the best mathematicians of the first two-thirds of the century devoted their efforts entirely to pure mathe matics. In the last third, however, the powerful methods devised by then for higher-dimensional problems were turned onto applications, and the tools of applied mathematics were drastically changed. By the end of the century, the temporary overemphasis on pure mathematics was completely gone and the traditional interconnections between pure mathematics and applications restored. "This century also saw the first primitive beginnings of the electronic calculator, whose development in the next century led to our modern methods of handling mathematics.

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.

Download or read book General Relativity Black hole astrophysics written by W. Israel and published by . This book was released on 2010 with total page 1064 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book A Derivation of Einstein s Field Equations from Linear Approximations for Undergraduate Physics Students written by Mark K. Clare and published by . This book was released on 1983 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Beyond Partial Differential Equations written by Horst Reinhard Beyer and published by Springer. This book was released on 2007-04-10 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.

Download or read book Astronomy and Astrophysics Abstracts written by S. Böhme and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: Astronomy and Astrophysics Abstracts has appeared in semi-annual volumes since 1969 and it has already become one of the fundamental publications in the fields of astronomy, astrophysics and neighbouring sciences. It is the most important English-language abstracting journal in the mentioned branches. ... The abstracts are classified under more than hundred subject categories, thus permitting a quick survey of the whole extended material. The AAA is a valuable and important publication for all students and scientists working in the fields of astronomy and related sciences. As such it represents a necessary ingredient of any astronomical library all over the world." Space Science Reviews #1 "Dividing the whole field plus related subjects into 108 categories, each work is numbered and most are accompanied by brief abstracts. Fairly comprehensive cross-referencing links relevant papers to more than one category, and exhaustive author and subject indices are to be found at the back, making the catalogues easy to use. The series appears to be so complete in its coverage and always less than a year out of date that I shall certainly have to make a little more space on those shelves for future volumes." The Observatory Magazine #1

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Download or read book Nonlinear Waves written by Lokenath Debnath and published by CUP Archive. This book was released on 1983-12-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.

Download or read book Relativity in Modern Physics written by Nathalie Deruelle and published by Oxford University Press. This book was released on 2018-08-23 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook on relativity integrates Newtonian physics, special relativity and general relativity into a single book that emphasizes the deep underlying principles common to them all, yet explains how they are applied in different ways in these three contexts. Newton's ideas about how to represent space and time, his laws of dynamics, and his theory of gravitation established the conceptual foundation from which modern physics developed. Book I in this volume offers undergraduates a modern view of Newtonian theory, emphasizing those aspects needed for understanding quantum and relativistic contemporary physics. In 1905, Albert Einstein proposed a novel representation of space and time, special relativity. Book II presents relativistic dynamics in inertial and accelerated frames, as well as a detailed overview of Maxwell's theory of electromagnetism. This provides undergraduate and graduate students with the background necessary for studying particle and accelerator physics, astrophysics and Einstein's theory of general relativity. In 1915, Einstein proposed a new theory of gravitation, general relativity. Book III in this volume develops the geometrical framework in which Einstein's equations are formulated, and presents several key applications: black holes, gravitational radiation, and cosmology, which will prepare graduate students to carry out research in relativistic astrophysics, gravitational wave astronomy, and cosmology.

Download or read book Global Nonlinear Stability of Schwarzschild Spacetime Under Polarized Perturbations written by Jérémie Szeftel and published by Princeton University Press. This book was released on 2020-12-15 with total page 858 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essential mathematical insights into one of the most important and challenging open problems in general relativity—the stability of black holes One of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations. An affirmative answer to this question would provide strong theoretical support for the physical reality of black holes. In this book, Sergiu Klainerman and Jérémie Szeftel take a first important step toward solving the fundamental black hole stability problem in general relativity by establishing the stability of nonrotating black holes—or Schwarzschild spacetimes—under so-called polarized perturbations. This restriction ensures that the final state of evolution is itself a Schwarzschild space. Building on the remarkable advances made in the past fifteen years in establishing quantitative linear stability, Klainerman and Szeftel introduce a series of new ideas to deal with the strongly nonlinear, covariant features of the Einstein equations. Most preeminent among them is the general covariant modulation (GCM) procedure that allows them to determine the center of mass frame and the mass of the final black hole state. Essential reading for mathematicians and physicists alike, this book introduces a rich theoretical framework relevant to situations such as the full setting of the Kerr stability conjecture.