Einstein S Field Equations And Their Physical Implications
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Einstein S Field Equations And Their Physical Implications
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Author : Bernd G. Schmidt
language : en
Publisher: Springer
Release Date : 2008-01-11
Einstein S Field Equations And Their Physical Implications written by Bernd G. Schmidt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Mathematics categories.
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.
Einstein S Field Equations And Their Physical Implications
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Author : Bernd G. Schmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-02-18
Einstein S Field Equations And Their Physical Implications written by Bernd G. Schmidt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-18 with Mathematics categories.
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 Einstein Equations And The Large Scale Behavior Of Gravitational Fields
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Author : Piotr T. Chrusciel
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Einstein Equations And The Large Scale Behavior Of Gravitational Fields written by Piotr T. Chrusciel and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Exact Solutions Of Einstein S Field Equations
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Author : Hans Stephani
language : en
Publisher: Cambridge University Press
Release Date : 2009-09-24
Exact Solutions Of Einstein S Field Equations written by Hans Stephani and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-24 with Science categories.
A completely revised and updated edition of this classic text, covering important new methods and many recently discovered solutions. This edition contains new chapters on generation methods and their application, classification of metrics by invariants, and treatments of homothetic motions and methods from dynamical systems theory. It also includes colliding waves, inhomogeneous cosmological solutions, and spacetimes containing special subspaces.
Stability By Linearization Of Einstein S Field Equation
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Author : Lluís Bruna
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-25
Stability By Linearization Of Einstein S Field Equation written by Lluís Bruna and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-25 with Science categories.
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
On The Topology And Future Stability Of The Universe
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Author : Hans Ringström
language : en
Publisher: OUP Oxford
Release Date : 2013-05-23
On The Topology And Future Stability Of The Universe written by Hans Ringström and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-23 with Mathematics categories.
The standard starting point in cosmology is the cosmological principle; the assumption that the universe is spatially homogeneous and isotropic. After imposing this assumption, the only freedom left, as far as the geometry is concerned, is the choice of one out of three permissible spatial geometries, and one scalar function of time. Combining the cosmological principle with an appropriate description of the matter leads to the standard models. It is worth noting that these models yield quite a successful description of our universe. However, even though the universe may, or may not, be almost spatially homogeneous and isotropic, it is clear that the cosmological principle is not exactly satisfied. This leads to several questions. The most natural one concerns stability: given initial data corresponding to an expanding model of the standard type, do small perturbations give rise to solutions that are similar to the future? Another question concerns the shape of the universe: what are the restrictions if we only assume the universe to appear almost spatially homogeneous and isotropic to every observer? The main purpose of the book is to address these questions. However, to begin with, it is necessary to develop the general theory of the Cauchy problem for the Einstein-Vlasov equations. In order to to make the results accessible to researchers who are not mathematicians, but who are familiar with general relativity, the book contains an extensive prologue putting the results into a more general context.
Mathematical Theory Of Black Holes In Higher Dimensions
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Author : Petya Nedkova
language : en
Publisher: Springer Nature
Release Date : 2024-08-16
Mathematical Theory Of Black Holes In Higher Dimensions written by Petya Nedkova and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-16 with Science categories.
This book portraits the mathematical theory which lies behind black hole solutions in spacetimes with an extra dimension. Step by step the authors build a comprehensive picture of the main concepts and tools necessary to understand these geometries. In this way the book addresses questions like: How do we describe black holes in higher dimensions? How can we construct such geometries explicitly as exact solutions to the field equations? How many independent solutions can exist and how are they classified? The book concentrates on five-dimensional stationary and axisymmetric spacetimes in electro-vacuum and systematically introduces the most important black geometries which can arise in these settings. The authors follow the natural progress of the research area by initially describing the first results that were obtained intuitively and sparkled interest in the community. Then the elaborate mathematical techniques are introduced which allow to systematically construct exact black hole solutions. Topics like the integrability of the theory, the hidden symmetries of the field equations, the available Bäcklund transformations and solution generation techniques based on the inverse scattering method are covered. The last part of the book is devoted to uniqueness theorems showing how to classify the black hole spacetimes and distinguish the non-equivalent ones. The book is not just a mere collection of facts but a methodological description of the most important mathematical techniques and constructions in an active research area. The discussion is pedagogical and all the methods are demonstrated on a variety of examples. Most of the book is adapted to the level of a graduate student possessing a basic knowledge of general relativity and differential equations, and can serve as a practical guide for quickly acquiring the specific concepts and calculation techniques. Both authors have contributed to the research area by their original results, and share their own experience and perspective.
The Conformal Structure Of Space Times
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Author : Jörg Frauendiener
language : en
Publisher: Springer
Release Date : 2008-01-11
The Conformal Structure Of Space Times written by Jörg Frauendiener and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Science categories.
Causal relations, and with them the underlying null cone or conformal structure, form a basic ingredient in all general analytical studies of asymptotically flat space-time. The present book reviews these aspects from the analytical, geometrical and numerical points of view. Care has been taken to present the material in a way that will also be accessible to postgraduate students and nonspecialist reseachers from related fields.
Geometry Mechanics And Dynamics
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Author : Dong Eui Chang
language : en
Publisher: Springer
Release Date : 2015-04-16
Geometry Mechanics And Dynamics written by Dong Eui Chang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-16 with Mathematics categories.
This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.
Towards A Theory Of Spacetime Theories
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Author : Dennis Lehmkuhl
language : en
Publisher: Birkhäuser
Release Date : 2017-01-05
Towards A Theory Of Spacetime Theories written by Dennis Lehmkuhl and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-05 with Mathematics categories.
This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spacetime theories.” This work will be of interest to physicists, as well as philosophers and historians of science working with or interested in General Relativity and/or Space, Time and Gravitation more generally.