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3 1 Formalism In General Relativity
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Book Synopsis 3+1 Formalism in General Relativity by : Éric Gourgoulhon
Download or read book 3+1 Formalism in General Relativity written by Éric Gourgoulhon and published by Springer. This book was released on 2012-02-27 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis 3+1 Formalism in General Relativity by : Éric Gourgoulhon
Download or read book 3+1 Formalism in General Relativity written by Éric Gourgoulhon and published by Springer Science & Business Media. This book was released on 2012-02-29 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis 3+1 Formalism in General Relativity by : Éric Gourgoulhon
Download or read book 3+1 Formalism in General Relativity written by Éric Gourgoulhon and published by Springer. This book was released on 2012-03-14 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Relativity by : Thomas W. Baumgarte
Download or read book Numerical Relativity written by Thomas W. Baumgarte and published by Cambridge University Press. This book was released on 2010-06-24 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pedagogical introduction to numerical relativity for students and researchers entering the field, and interested scientists.
Book Synopsis Introduction to 3+1 Numerical Relativity by : Miguel Alcubierre
Download or read book Introduction to 3+1 Numerical Relativity written by Miguel Alcubierre and published by OUP Oxford. This book was released on 2008-04-10 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the modern field of 3+1 numerical relativity. The book has been written in a way as to be as self-contained as possible, and only assumes a basic knowledge of special relativity. Starting from a brief introduction to general relativity, it discusses the different concepts and tools necessary for the fully consistent numerical simulation of relativistic astrophysical systems, with strong and dynamical gravitational fields. Among the topics discussed in detail are the following: the initial data problem, hyperbolic reductions of the field equations, gauge conditions, the evolution of black hole space-times, relativistic hydrodynamics, gravitational wave extraction and numerical methods. There is also a final chapter with examples of some simple numerical space-times. The book is aimed at both graduate students and researchers in physics and astrophysics, and at those interested in relativistic astrophysics.
Book Synopsis Formulations of General Relativity by : Kirill Krasnov
Download or read book Formulations of General Relativity written by Kirill Krasnov and published by Cambridge University Press. This book was released on 2020-11-26 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advanced Lectures on General Relativity by : Geoffrey Compère
Download or read book Advanced Lectures on General Relativity written by Geoffrey Compère and published by Springer. This book was released on 2019-01-31 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The four topics covered are: Surface charges as conserved quantities in theories of gravity; Classical and holographic features of three-dimensional Einstein gravity; Asymptotically flat spacetimes in four dimensions: BMS group and memory effects; The Kerr black hole: properties at extremality and quasi-normal mode ringing. Each topic starts with historical foundations and points to a few modern research directions.
Book Synopsis Spacetime and Geometry by : Sean M. Carroll
Download or read book Spacetime and Geometry written by Sean M. Carroll and published by Cambridge University Press. This book was released on 2019-08-08 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
Book Synopsis Advanced General Relativity by : John Stewart
Download or read book Advanced General Relativity written by John Stewart and published by Cambridge University Press. This book was released on 1993-11-26 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to advanced general relativity.
Book Synopsis Elements of General Relativity by : Piotr T. Chruściel
Download or read book Elements of General Relativity written by Piotr T. Chruściel and published by Springer Nature. This book was released on 2020-03-19 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematics and physics of general relativity, its basic physical concepts, its observational implications, and the new insights obtained into the nature of space-time and the structure of the universe. It introduces some of the most striking aspects of Einstein's theory of gravitation: black holes, gravitational waves, stellar models, and cosmology. It contains a self-contained introduction to tensor calculus and Riemannian geometry, using in parallel the language of modern differential geometry and the coordinate notation, more familiar to physicists. The author has strived to achieve mathematical rigour, with all notions given careful mathematical meaning, while trying to maintain the formalism to the minimum fit-for-purpose. Familiarity with special relativity is assumed. The overall aim is to convey some of the main physical and geometrical properties of Einstein's theory of gravitation, providing a solid entry point to further studies of the mathematics and physics of Einstein equations.
Book Synopsis General Relativity by : I. R. Kenyon
Download or read book General Relativity written by I. R. Kenyon and published by Oxford University Press, USA. This book was released on 1990 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Einstein's general theory of relativity is perhaps the most important perspective to emerge in a century of astonishing progress in the field of physics. However, it is also a notoriously difficult subject for beginning students. This book describes general relativity in terms understandable to undergraduates in physics and astronomy. It discusses concepts and experimental results, and provides a succinct account of formalism. A brief review of special relativity is followed by a discussion of the equivalence principle and its implications. Other topics covered include concepts of curvature and the Schwarzschild metric, tests of the theory of relativity, black holes and their properties, gravitational radiation and methods for its detection, the impact of general relativity on cosmology, and the continuing search for a quantum theory of gravity. A set of worked examples, background appendices, and an annotated bibliography are also included. Written at a level accessible to nonspecialists, this book is especially strong on the experimental physics of relativity.
Book Synopsis A First Course in General Relativity by : Bernard F. Schutz
Download or read book A First Course in General Relativity written by Bernard F. Schutz and published by Cambridge University Press. This book was released on 1985-01-31 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis General Relativity by : Michael Paul Hobson
Download or read book General Relativity written by Michael Paul Hobson and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for advanced undergraduate and graduate students, this is a clear mathematical introduction to Einstein's theory of general relativity and its physical applications. Concentrating on the theory's physical consequences, this approachable textbook contains over 300 exercises to illuminate and extend the discussion.
Book Synopsis The Potential of Fields in Einstein's Theory of Gravitation by : Zafar Ahsan
Download or read book The Potential of Fields in Einstein's Theory of Gravitation written by Zafar Ahsan and published by Springer. This book was released on 2019-07-17 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed study of the Lanczos potential in general relativity by using tetrad formalisms. It demonstrates that these formalisms offer some simplifications over the tensorial methods, and investigates a general approach to finding the Lanczos potential for algebraic space–time by translating all the tensorial relations concerning the Lanczos potential into the language of tetrad formalisms and using the Newman–Penrose and Geroch–Held–Penrose formalisms. In addition, the book obtains the Lanczos potential for perfect fluid space–time, and applies the results to cosmological models of the universe. In closing, it highlights other methods, apart from tetrad formalisms, for finding the Lanczos potential, as well as further applications of the Newman–Penrose formalism. Given its scope, the book will be of interest to pure mathematicians, theoretical physicists and cosmologists, and will provide common ground for communication among these scientific communities.
Book Synopsis Introduction to General Relativity by : Cosimo Bambi
Download or read book Introduction to General Relativity written by Cosimo Bambi and published by Springer. This book was released on 2018-06-18 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the approach of Lev Landau and Evgenii Lifshitz, this book introduces the theory of special and general relativity with the Lagrangian formalism and the principle of least action. This method allows the complete theory to be constructed starting from a small number of assumptions, and is the most natural approach in modern theoretical physics. The book begins by reviewing Newtonian mechanics and Newtonian gravity with the Lagrangian formalism and the principle of least action, and then moves to special and general relativity. Most calculations are presented step by step, as is done on the board in class. The book covers recent advances in gravitational wave astronomy and provides a general overview of current lines of research in gravity. It also includes numerous examples and problems in each chapter.
Book Synopsis Tetrad Formalism for Exact Cosmological Observables by : Ermis Mitsou
Download or read book Tetrad Formalism for Exact Cosmological Observables written by Ermis Mitsou and published by Springer Nature. This book was released on 2020-06-25 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel mathematical formalism, based on the tetrad formulation of differential geometry, for describing cosmological observables exactly and conveniently. It covers all the standard observables, i.e. distances, weak lensing, number counts and cosmic microwave background, and also includes a detailed derivation of general-relativistic matrix kinetic theory. All the fully nonlinear equations are derived in detail and the mathematical content is self-contained, so that readers require only a basic knowledge of general relativity. Moreover, the authors discuss several subtle issues that are usually overlooked in the literature and, in particular, issues that distinguish this formalism from the more approximative standard practice.
Book Synopsis The Theory of Space, Time and Gravitation by : V. Fock
Download or read book The Theory of Space, Time and Gravitation written by V. Fock and published by Elsevier. This book was released on 2015-08-11 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Theory of Space, Time, and Gravitation, 2nd Revised Edition focuses on Relativity Theory and Einstein's Theory of Gravitation and correction of the misinterpretation of the Einsteinian Gravitation Theory. The book first offers information on the theory of relativity and the theory of relativity in tensor form. Discussions focus on comparison of distances and lengths in moving reference frames; comparison of time differences in moving reference frames; position of a body in space at a given instant in a fixed reference frame; and proof of the linearity of the transformation linking two inertial frames. The text then ponders on general tensor analysis, including permissible transformations for space and time coordinates, parallel transport of a vector, covariant differentiation, and basic properties of the curvature tensor. The publication examines the formulation of relativity theory in arbitrary coordinates and principles of the theory of gravitation. Topics include equations of mathematical physics in arbitrary coordinates; integral form of the conservation laws in arbitrary coordinates; variational principle and the energy tensor; and comparison with the statement of the problem in Newtonian theory. The manuscript is a dependable reference for readers interested in the theory of space, time, and gravitation.
