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Author: F. G. Friedlander
Publisher: Cambridge University Press
ISBN: 0521205670
Category : Science
Languages : en
Pages : 298
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Book Description
This book gives a rigourous discussion of the local effects of curvature on the behaviour of waves. In the course of this discussion many techniques are developed which are also needed for a study of more general problems, in which the gravitational field itself plays a dynamical role.
Author: F. G. Friedlander
Publisher: Cambridge University Press
ISBN: 0521205670
Category : Science
Languages : en
Pages : 298
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Book Description
This book gives a rigourous discussion of the local effects of curvature on the behaviour of waves. In the course of this discussion many techniques are developed which are also needed for a study of more general problems, in which the gravitational field itself plays a dynamical role.
Author: Friedrich G. Friedlander
Publisher:
ISBN:
Category :
Languages : en
Pages : 282
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Book Description
Author: Stephen W. Hawking
Publisher: Cambridge University Press
ISBN: 1009253182
Category : Science
Languages : en
Pages : 414
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Book Description
First published in 1973, this influential work discusses Einstein's General Theory of Relativity to show how two of its predictions arise: first, that the ultimate fate of many massive stars is to undergo gravitational collapse to form 'black holes'; and second, that there was a singularity in the past at the beginning of the universe. Starting with a precise formulation of the theory, including the necessary differential geometry, the authors discuss the significance of space-time curvature and examine the properties of a number of exact solutions of Einstein's field equations. They develop the theory of the causal structure of a general space-time, and use it to prove a number of theorems establishing the inevitability of singularities under certain conditions. A Foreword contributed by Abhay Ashtekar and a new Preface from George Ellis help put the volume into context of the developments in the field over the past fifty years.
Author: Abhay Ashtekar
Publisher: Cambridge University Press
ISBN: 110703731X
Category : Science
Languages : en
Pages : 697
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Book Description
Explore spectacular advances in contemporary physics with this unique celebration of the centennial of Einstein's discovery of general relativity.
Author: David Ellwood
Publisher: American Mathematical Soc.
ISBN: 0821868616
Category : Mathematics
Languages : en
Pages : 587
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Book Description
This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Author: Michael Ruzhansky
Publisher: Springer Science & Business Media
ISBN: 3034804547
Category : Mathematics
Languages : en
Pages : 327
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Book Description
Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. This volume aims to collect some recent advances in the area in order to allow a quick overview of ongoing research. The contributors are first rate mathematicians. This collection of research papers is centred around parametrix constructions and microlocal analysis; asymptotic constructions of solutions; energy and dispersive estimates; and associated spectral transforms. Applications concerning elasticity and general relativity complement the volume. The book gives an overview of a variety of ongoing current research in the field and, therefore, allows researchers as well as students to grasp new aspects and broaden their understanding of the area.
Author: Tomás Ortín
Publisher: Cambridge University Press
ISBN: 1316239578
Category : Science
Languages : en
Pages : 1043
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Book Description
Self-contained and comprehensive, this definitive new edition of Gravity and Strings is a unique resource for graduate students and researchers in theoretical physics. From basic differential geometry through to the construction and study of black-hole and black-brane solutions in quantum gravity - via all the intermediate stages - this book provides a complete overview of the intersection of gravity, supergravity, and superstrings. Now fully revised, this second edition covers an extensive array of topics, including new material on non-linear electric-magnetic duality, the electric-tensor formalism, matter-coupled supergravity, supersymmetric solutions, the geometries of scalar manifolds appearing in 4- and 5-dimensional supergravities, and much more. Covering reviews of important solutions and numerous solution-generating techniques, and accompanied by an exhaustive index and bibliography, this is an exceptional reference work.
Author: Bei-Lok B. Hu
Publisher: Cambridge University Press
ISBN: 0521193575
Category : Science
Languages : en
Pages : 615
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Book Description
An overview of semi-classical gravity theory and stochastic gravity as theories of quantum gravity in curved space-time.
Author: R. S. Ward
Publisher: Cambridge University Press
ISBN: 9780521422680
Category : Mathematics
Languages : en
Pages : 534
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Book Description
Deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, and several complex variables.
Author: Tiberiu Harko
Publisher: Cambridge University Press
ISBN: 1108584578
Category : Science
Languages : en
Pages : 476
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Book Description
Recent cosmological observations have posed a challenge for traditional theories of gravity: what is the force driving the accelerated expansion of the universe? What if dark energy or dark matter do not exist and what we observe is a modification of the gravitational interaction that dominates the universe at large scales? Various extensions to Einstein's General Theory of Relativity have been proposed, and this book presents a detailed theoretical and phenomenological analysis of several leading, modified theories of gravity. Theories with generalised curvature-matter couplings are first explored, followed by hybrid metric-Palatini gravity. This timely book first discusses key motivations behind the development of these modified gravitational theories, before presenting a detailed overview of their subsequent development, mathematical structure, and cosmological and astrophysical implications. Covering recent developments and with an emphasis on astrophysical and cosmological applications, this is the perfect text for graduate students and researchers.
