3 1 Formalism In General Relativity
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Author |
: Éric Gourgoulhon |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 304 |
Release |
: 2012-02-29 |
ISBN-10 |
: 9783642245244 |
ISBN-13 |
: 3642245242 |
Rating |
: 4/5 (44 Downloads) |
Synopsis 3+1 Formalism in General Relativity by : Éric Gourgoulhon
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 |
: Miguel Alcubierre |
Publisher |
: Oxford University Press |
Total Pages |
: 459 |
Release |
: 2008-04-10 |
ISBN-10 |
: 9780199205677 |
ISBN-13 |
: 0199205671 |
Rating |
: 4/5 (77 Downloads) |
Synopsis Introduction to 3+1 Numerical Relativity by : Miguel Alcubierre
This book is a self-contained introduction to the field of numerical relativity. Starting from basic general relativity, it introduces all the concepts and tools necessary for the fully relativistic simulation of astrophysical systems with strong and dynamical gravitational fields.
Author |
: Thomas W. Baumgarte |
Publisher |
: Cambridge University Press |
Total Pages |
: 717 |
Release |
: 2010-06-24 |
ISBN-10 |
: 9781139643177 |
ISBN-13 |
: 1139643177 |
Rating |
: 4/5 (77 Downloads) |
Synopsis Numerical Relativity by : Thomas W. Baumgarte
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 |
: Raymond Brian Burston |
Publisher |
: |
Total Pages |
: 176 |
Release |
: 2005 |
ISBN-10 |
: OCLC:225200690 |
ISBN-13 |
: |
Rating |
: 4/5 (90 Downloads) |
Synopsis 3+1 Perturbation Formalism for General Relativity by : Raymond Brian Burston
Author |
: Kirill Krasnov |
Publisher |
: Cambridge University Press |
Total Pages |
: 391 |
Release |
: 2020-11-26 |
ISBN-10 |
: 9781108481649 |
ISBN-13 |
: 1108481647 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Formulations of General Relativity by : Kirill Krasnov
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 |
: Sean M. Carroll |
Publisher |
: Cambridge University Press |
Total Pages |
: 529 |
Release |
: 2019-08-08 |
ISBN-10 |
: 9781108488396 |
ISBN-13 |
: 1108488390 |
Rating |
: 4/5 (96 Downloads) |
Synopsis Spacetime and Geometry by : Sean M. Carroll
An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
Author |
: John Stewart |
Publisher |
: Cambridge University Press |
Total Pages |
: 244 |
Release |
: 1993-11-26 |
ISBN-10 |
: 0521449464 |
ISBN-13 |
: 9780521449465 |
Rating |
: 4/5 (64 Downloads) |
Synopsis Advanced General Relativity by : John Stewart
A self-contained introduction to advanced general relativity.
Author |
: Farook Rahaman |
Publisher |
: Cambridge University Press |
Total Pages |
: 428 |
Release |
: 2021-09-30 |
ISBN-10 |
: 9781009032377 |
ISBN-13 |
: 1009032372 |
Rating |
: 4/5 (77 Downloads) |
Synopsis The General Theory of Relativity by : Farook Rahaman
The book aims to expound the general theory of relativity with a mathematical point of view. Catering to the needs of postgraduate students and researchers in the field of astrophysics and mathematical physics, it offers the readers a comprehensive understanding of the advanced topics of the subject matter. It specifically discusses the mathematical foundation of tensor calculus, gives a background of geodesics, Einstein's field equations, linearised gravity, spacetime of spherically symmetric distribution of matter and black holes, and particle and photon orbits in spacetime. Apart from the formulation of general relativity, Lie derivatives and its applications, and causality of spacetime are also discussed in detail. Certain preliminary concepts of extrinsic curvature, Lagrangian formalism of general theory of relativity and 3 + 1 decomposition of space-time are covered and are provided in the book as appendices.
Author |
: R.K. Sachs |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 302 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461299035 |
ISBN-13 |
: 1461299039 |
Rating |
: 4/5 (35 Downloads) |
Synopsis General Relativity for Mathematicians by : R.K. Sachs
This is a book about physics, written for mathematicians. The readers we have in mind can be roughly described as those who: I. are mathematics graduate students with some knowledge of global differential geometry 2. have had the equivalent of freshman physics, and find popular accounts of astrophysics and cosmology interesting 3. appreciate mathematical elarity, but are willing to accept physical motiva tions for the mathematics in place of mathematical ones 4. are willing to spend time and effort mastering certain technical details, such as those in Section 1. 1. Each book disappoints so me readers. This one will disappoint: 1. physicists who want to use this book as a first course on differential geometry 2. mathematicians who think Lorentzian manifolds are wholly similar to Riemannian ones, or that, given a sufficiently good mathematical back ground, the essentials of a subject !ike cosmology can be learned without so me hard work on boring detaiis 3. those who believe vague philosophical arguments have more than historical and heuristic significance, that general relativity should somehow be "proved," or that axiomatization of this subject is useful 4. those who want an encyclopedic treatment (the books by Hawking-Ellis [1], Penrose [1], Weinberg [1], and Misner-Thorne-Wheeler [I] go further into the subject than we do; see also the survey article, Sachs-Wu [1]). 5. mathematicians who want to learn quantum physics or unified fieId theory (unfortunateIy, quantum physics texts all seem either to be for physicists, or merely concerned with formaI mathematics).
Author |
: Miguel Alcubierre |
Publisher |
: OUP Oxford |
Total Pages |
: 464 |
Release |
: 2008-04-10 |
ISBN-10 |
: 9780191548291 |
ISBN-13 |
: 0191548294 |
Rating |
: 4/5 (91 Downloads) |
Synopsis Introduction to 3+1 Numerical Relativity by : Miguel Alcubierre
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.