3 1 Formalism In General Relativity

Author : Éric Gourgoulhon
Publisher : Springer
ISBN 13 : 3642245250
Total Pages : 304 pages
Book Rating : 4.51/5 ( download)

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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 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.

Author : Éric Gourgoulhon
Publisher : Springer Science & Business Media
ISBN 13 : 3642245242
Total Pages : 304 pages
Book Rating : 4.44/5 ( download)

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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.

Author : Éric Gourgoulhon
Publisher : Springer
ISBN 13 : 9783642245268
Total Pages : 294 pages
Book Rating : 4.69/5 ( download)

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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.

Author : Thomas W. Baumgarte
Publisher : Cambridge University Press
ISBN 13 : 1139643177
Total Pages : 717 pages
Book Rating : 4.77/5 ( download)

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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: Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, the book develops the mathematical formalism from first principles, and then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. The book contains 300 exercises to help readers master new material as it is presented. Numerous illustrations, many in color, assist in visualizing new geometric concepts and highlighting the results of computer simulations. Summary boxes encapsulate some of the most important results for quick reference. Applications covered include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and other topics of current physical and astrophysical significance.

Author : Miguel Alcubierre
Publisher : OUP Oxford
ISBN 13 : 0191548294
Total Pages : 464 pages
Book Rating : 4.91/5 ( download)

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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.

Author : Kirill Krasnov
Publisher : Cambridge University Press
ISBN 13 : 1108481647
Total Pages : 391 pages
Book Rating : 4.49/5 ( download)

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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.

Author : Cosimo Bambi
Publisher : Springer
ISBN 13 : 9811310904
Total Pages : 335 pages
Book Rating : 4.04/5 ( download)

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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.

Author : Geoffrey Compère
Publisher : Springer
ISBN 13 : 303004260X
Total Pages : 140 pages
Book Rating : 4.08/5 ( download)

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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.

Author : John Stewart
Publisher : Cambridge University Press
ISBN 13 : 9780521449465
Total Pages : 244 pages
Book Rating : 4.64/5 ( download)

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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.

Author : Sean M. Carroll
Publisher : Cambridge University Press
ISBN 13 : 1108488390
Total Pages : 529 pages
Book Rating : 4.96/5 ( download)

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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.