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 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.
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.
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.
Einstein Equations Local Energy Self Force And Fields In General Relativity
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Author : Sergio Luigi Cacciatori
language : en
Publisher: Springer Nature
Release Date : 2023-03-15
Einstein Equations Local Energy Self Force And Fields In General Relativity written by Sergio Luigi Cacciatori and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-15 with Mathematics categories.
This volume guides early-career researchers through recent breakthroughs in mathematics and physics as related to general relativity. Chapters are based on courses and lectures given at the July 2019 Domoschool, International Alpine School in Mathematics and Physics, held in Domodossola, Italy, which was titled “Einstein Equations: Physical and Mathematical Aspects of General Relativity”. Structured in two parts, the first features four courses from prominent experts on topics such as local energy in general relativity, geometry and analysis in black hole spacetimes, and antimatter gravity. The second part features a variety of papers based on talks given at the summer school, including topics like: Quantum ergosphere General relativistic Poynting-Robertson effect modelling Numerical relativity Length-contraction in curved spacetime Classicality from an inhomogeneous universe Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity will be a valuable resource for students and researchers in mathematics and physicists interested in exploring how their disciplines connect to general relativity.
100 Years Of Gravity And Accelerated Frames
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Author : Jong-Ping Hsu
language : en
Publisher: World Scientific
Release Date : 2005
100 Years Of Gravity And Accelerated Frames written by Jong-Ping Hsu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
This collection of papers presents ideas and problems arising over the past 100 years regarding classical and quantum gravity, gauge theories of gravity, and spacetime transformations of accelerated frames. Both Einstein''s theory of gravity and the YangOCoMills theory are gauge invariant. The invariance principles in physics have transcended both kinetic and dynamic properties and are at the very heart of our understanding of the physical world. In this spirit, this book attempts to survey the development of various formulations for gravitational and YangOCoMills fields and spacetime transformations of accelerated frames, and to reveal their associated problems and limitations. The aim is to present some of the leading ideas and problems discussed by physicists and mathematicians. We highlight three aspects: formulations of gravity as a YangOCoMills field, first discussed by Utiyama; problems of gravitational theory, discussed by Feynman, Dyson and others; spacetime properties and the physics of fields and particles in accelerated frames of reference. These unfulfilled aspects of Einstein and YangOCoMills'' profound thoughts present a great challenge to physicists and mathematicians in the 21st century."
Criticisms Of The Einstein Field Equation
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Author : Myron Evans
language : en
Publisher: Cambridge International Science Publishing
Release Date : 2011
Criticisms Of The Einstein Field Equation written by Myron Evans and has been published by Cambridge International Science Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
In about 1915, Einstein and Hilbert independently inferred a field equation of general relativity based on the geometry then known to them. Almost since inception this equation was criticised by prominent physicists and mathematicians, notably Schroedinger (1918) and Cartan (early twenties). The latter clearly informed Einstein that the type of geometry that he used had a fundamental error in it, it omitted consideration of a quantity known as spacetime torsion and used the wrong symmetry for the geometrical connection. These criticisms were brushed aside when Eddington claimed to have verified a prediction of the theory, the angle of deflection of light grazing the sun was twice the Newtonian value. It is well known by now that this claim by Eddington was subjective, the usual mistake was made of choosing data to fit a theory. It finally became clear that the field equation is hopelessly incorrect when the velocity curves of spiral galaxies were discovered in the late fifties. About that time a new generation of mathematicians and theoretical physicists began to elevate the Einstein field equation into the realms of pure mythology, it was claimed to have produced "big bang" (a derisory term coined by Sir Fred Hoyle). It is now known experimentally that this claim is again hopelessly wrong. So there is a domino effect going on, all that is known about the universe is totally wrong as one BBC programme put it recently. The reason for this is the use of the wrong type of geometry by Einstein, right at the beginning of the subject. In 2003 one of the four authors of this book began to construct a unified field theory of general relativity called "Einstein Cartan Evans" or ECE theory. This time, the geometry was correct, and physics was based on torsion. The ECE theory has developed into about 168 source papers to date and several books and articles by ECE scholars. It has made a phenomenal worldwide impact, indicating a great dissatisfaction with the obsolete physics. This book is the first to collect the severe criticisms of Einstein that are now commonplace. Not only have cosmologists adhered to an incorrect geometry, like glue stuck to marble, but they have also compounded this error by using incorrect methods of solution of an incorrect equation. The result is, unsurprisingly, totally wrong. One of the four authors of this book is the most severe and tenacious critic of these methods, Stephen Crothers, whose careful scholarship has unearthed some amazing mistakes repeated in perpetuity. The first chapter is an introduction by Myron Evans, and in the second chapter he summarizes the development of ECE theory. The third chapter is by Stephen Crothers, and summarizes his numerous criticisms of the incorrect methods of Einsteinian cosmology, criticisms made with characteristic intellectual honesty for more than a decade.The fourth chapter is by Horst Eckardt, who makes use of computer algebra and the Evans Identity of geometry to show that all the metrics that are solutions of the Einstein field equation are incorrect due to neglect of torsion. The computer algebra ensures correctness and is the only way to deal with the often bizarre complexity of the meaningless and obsolete physics that grew like detritus around the Einstein field equation. The fifth chapter is by one of the leading astronomers in Britain, Kerry Pendergast, who gives a readable account of the new post Einsteinian astronomy, how ECE theory should be used in astronomy and how to come to grips with Hawking's sudden abandonment of his big bang theory in 2005.
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.
A Mathematical Journey To Relativity
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Author : Wladimir-Georges Boskoff
language : en
Publisher: Springer Nature
Release Date : 2020-06-01
A Mathematical Journey To Relativity written by Wladimir-Georges Boskoff and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-01 with Science categories.
This book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.