How Einstein Found His Field Equations
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How Einstein Found His Field Equations
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Author : Michel Janssen
language : en
Publisher: Springer Nature
Release Date : 2022-07-29
How Einstein Found His Field Equations written by Michel Janssen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-29 with Science categories.
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.
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 paperback edition of a classic text, this book contains six new chapters, covering generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics.
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.
Einstein S Field Equations And Their Physical Implications
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Author : Bernd G. Schmidt
language : en
Publisher: Springer
Release Date : 2014-03-12
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 2014-03-12 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.
Beyond Einstein Gravity
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Author : Jorge Ovalle
language : en
Publisher: Springer Nature
Release Date : 2020-01-16
Beyond Einstein Gravity written by Jorge Ovalle and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-16 with Science categories.
This book serves two main purposes: firstly, it shows, in a simple way, how the possible existence of an extra-spatial dimension would affect the predictions of four-dimensional General Relativity, a model known as the Brane world; secondly, it explains, step-by-step, a new technique called Minimal Geometric Deformation, which was introduced for the purpose of solving the correspondingly modified Einstein field equations. This method gave rise to the Gravitational Decoupling in General Relativity, which is widely used to solve the Einstein field equations in various contexts.
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
Einstein S General Theory Of Relativity
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Author : Øyvind Grøn
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-04
Einstein S General Theory Of Relativity written by Øyvind Grøn 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 2007-05-04 with Science categories.
This book introduces the general theory of relativity and includes applications to cosmology. The book provides a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, the authors offer a thorough presentation of the theory of relativity. Also included are some advanced topics not previously covered by textbooks, including Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will benefit from an updated introduction to general relativity including the most recent developments in cosmology.
The Universe Of General Relativity
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Author : A.J. Kox
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-10
The Universe Of General Relativity written by A.J. Kox 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 2006-09-10 with Science categories.
Outgrowth of 6th Int'l Conference on the History of General Relativity, held in Amsterdam on June 26-29, 2002 Contributions from notable experts offer both new and historical insights on gravitation, general relativity, cosmology, unified field theory, and the history of science Topics run gamet from detailed mathematical discussions to more personal recollections of relativity as seen through the eyes of the public and renowned relativists
Einstein Hilbert And The Theory Of Gravitation
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Author : Jagdish Mehra
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Einstein Hilbert And The Theory Of Gravitation written by Jagdish Mehra 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 2012-12-06 with Science categories.
Some time ago I published a small piece * dealing with a charming little essay on 'the state of ether in magnetic fields', which the sixteen-year-old Einstein had written while he was awaiting admission to the E. T. H. in Zurich. This paper sought to trace the continuity between Einstein's early interest in electrodynamics and his later work on the special and general relativity theories. On reading this paper, Professor Eugene Wigner asked me whether David Hilbert had not independently discovered the field equations of gravitation. ** His impression from his stay in Gottingen (where Wigner had been Hilbert's assistant for one year in the late nineteen-twenties) was that Hilbert had indeed done so, and he asked me if it was true. I replied to Professor Wigner about Hilbert's contribution to the theory of gravitation. t He kindly encouraged me to expand my account to deal with the intricate and exciting details of the early years in the formulation of the general relativity theory of gravitation. This is what I have sought to do in this study. Albert Einstein created the general relativity theory of gravitation and dominated its development through the rest of his life. His early work on the theory of gravitation, from 1912 to 1916, had the drama of high adventure. It culminated in the establishment of its foundations which have remained unassailed by the theoretical and experimental work of succeeding decades.
General Relativity
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Author : Hans Stephani
language : en
Publisher: Cambridge University Press
Release Date : 1990-06-29
General Relativity 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 1990-06-29 with Science categories.
This is an excellent introduction to the subjects of gravitation and space-time structure. It discusses the foundations of Riemann geometry; the derivation of Einstein field equations; linearised theory; far fields and gravitational waves; the invariant characterisation of exact solutions; gravitational collapse; cosmology as well as alternative gravitational theories and the problem of quantum gravity.