Formulations Of General Relativity
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Formulations Of General Relativity
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Author : Kirill Krasnov
language : en
Publisher: Cambridge University Press
Release Date : 2020-11-26
Formulations Of General Relativity written by Kirill Krasnov 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 2020-11-26 with Science categories.
Carefully documenting the different formulations of general relativity, the author reveals valuable insight into the nature of the gravitational force and its interaction with matter. This book will interest graduate students and researchers in the fields of general relativity, gravitational physics and differential geometry.
Advanced General Relativity
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Author : John Stewart
language : en
Publisher: Cambridge University Press
Release Date : 1993-11-26
Advanced General Relativity written by John Stewart 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 1993-11-26 with Science categories.
A self-contained introduction to advanced general relativity.
3 1 Formalism In General Relativity
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Author : Éric Gourgoulhon
language : en
Publisher: Springer
Release Date : 2012-02-27
3 1 Formalism In General Relativity written by Éric Gourgoulhon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-27 with Science categories.
This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.
Group Theory And General Relativity
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Author : Moshe Carmeli
language : en
Publisher: World Scientific
Release Date : 2000
Group Theory And General Relativity written by Moshe Carmeli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.
This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory. There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups -- particularly the Lorentz and the SL(2, C) groups -- to the theory of general relativity. Each chapter is concluded with a set of problems. The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2, C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed. The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.
A Relativist S Toolkit
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Author : Eric Poisson
language : en
Publisher: Cambridge University Press
Release Date : 2004-05-06
A Relativist S Toolkit written by Eric Poisson 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 2004-05-06 with Science categories.
This 2004 textbook fills a gap in the literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most elegant, successful, and relevant applications of general relativity. Among the topics discussed are congruencies of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity. Although the book is self-contained, it is not meant to serve as an introduction to general relativity. Instead, it is meant to help the reader acquire advanced skills and become a competent researcher in relativity and gravitational physics. The primary readership consists of graduate students in gravitational physics. It will also be a useful reference for more seasoned researchers working in this field.
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."
Exact Space Times In Einstein S General Relativity
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Author : Jerry B. Griffiths
language : en
Publisher: Cambridge University Press
Release Date : 2009-10-15
Exact Space Times In Einstein S General Relativity written by Jerry B. Griffiths 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 2009-10-15 with Science categories.
Einstein's theory of general relativity is a theory of gravity and, as in the earlier Newtonian theory, much can be learnt about the character of gravitation and its effects by investigating particular idealised examples. This book describes the basic solutions of Einstein's equations with a particular emphasis on what they mean, both geometrically and physically. Concepts such as big bang and big crunch-types of singularities, different kinds of horizons and gravitational waves, are described in the context of the particular space-times in which they naturally arise. These notions are initially introduced using the most simple and symmetric cases. Various important coordinate forms of each solution are presented, thus enabling the global structure of the corresponding space-time and its other properties to be analysed. The book is an invaluable resource both for graduate students and academic researchers working in gravitational physics.
A First Course In General Relativity
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Author : Bernard F. Schutz
language : en
Publisher: Cambridge University Press
Release Date : 1985-01-31
A First Course In General Relativity written by Bernard F. Schutz 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 1985-01-31 with Science categories.
This textbook develops general relativity and its associated mathematics from a minimum of prerequisites, leading to a physical understanding of the theory in some depth.
The Problem Of Time
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Author : Edward Anderson
language : en
Publisher: Springer
Release Date : 2017-09-18
The Problem Of Time written by Edward Anderson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-18 with Science categories.
This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon entertaining background independence in classical (rather than quantum) physics. By this development, and interpreting shape theory as modelling background independence, this book further establishes background independence as a field of study. Background independent mechanics, as well as minisuperspace (spatially homogeneous) models of GR and perturbations thereabout are used to illustrate these points. As hitherto formulated, the different facets of the Problem of Time greatly interfere with each others' attempted resolutions. This book explains how, none the less, a local resolution of the Problem of Time can be arrived at after various reconceptualizations of the facets and reformulations of their mathematical implementation. Self-contained appendices on mathematical methods for basic and foundational quantum gravity are included. Finally, this book outlines how supergravity is refreshingly different from GR as a realization of background independence, and what background independence entails at the topological level and beyond.
Introduction To General Relativity And Cosmology
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Author : Christian G Boehmer
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-10-06
Introduction To General Relativity And Cosmology written by Christian G Boehmer and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-06 with Science categories.
Introduction to General Relativity and Cosmology gives undergraduate students an overview of the fundamental ideas behind the geometric theory of gravitation and spacetime. Through pointers on how to modify and generalise Einstein's theory to enhance understanding, it provides a link between standard textbook content and current research in the field.Chapters present complicated material practically and concisely, initially dealing with the mathematical foundations of the theory of relativity, in particular differential geometry. This is followed by a discussion of the Einstein field equations and their various properties. Also given is analysis of the important Schwarzschild solutions, followed by application of general relativity to cosmology. Questions with fully worked answers are provided at the end of each chapter to aid comprehension and guide learning. This pared down textbook is specifically designed for new students looking for a workable, simple presentation of some of the key theories in modern physics and mathematics.