Analytical And Numerical Approaches To Mathematical Relativity PDF Download
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Author | : Jörg Frauendiener |
Publisher | : Springer |
Total Pages | : 281 |
Release | : 2009-09-02 |
Genre | : Science |
ISBN | : 9783540819288 |
Download Analytical and Numerical Approaches to Mathematical Relativity Book in PDF, ePub and Kindle
General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.
Author | : Jörg Frauendiener |
Publisher | : Springer |
Total Pages | : 288 |
Release | : 2006-03-28 |
Genre | : Science |
ISBN | : 354033484X |
Download Analytical and Numerical Approaches to Mathematical Relativity Book in PDF, ePub and Kindle
General relativity ranks among the most accurately tested fundamental theories in all of physics. Deficiencies in mathematical and conceptual understanding still exist, hampering further progress. This book collects surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods.
Author | : Thomas W. Baumgarte |
Publisher | : Cambridge University Press |
Total Pages | : 717 |
Release | : 2010-06-24 |
Genre | : Science |
ISBN | : 1139643177 |
Download Numerical Relativity Book in PDF, ePub and Kindle
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 | : Christian Klein |
Publisher | : Springer |
Total Pages | : 249 |
Release | : 2009-09-02 |
Genre | : Science |
ISBN | : 9783540814948 |
Download Ernst Equation and Riemann Surfaces Book in PDF, ePub and Kindle
Exact solutions to Einstein’s equations have been useful for the understanding of general relativity in many respects. They have led to such physical concepts as black holes and event horizons, and helped to visualize interesting features of the theory. This volume studies the solutions to the Ernst equation associated to Riemann surfaces in detail. In addition, the book discusses the physical and mathematical aspects of this class analytically as well as numerically.
Author | : Christian Klein |
Publisher | : Springer Science & Business Media |
Total Pages | : 274 |
Release | : 2005-11-18 |
Genre | : Science |
ISBN | : 9783540285892 |
Download Ernst Equation and Riemann Surfaces Book in PDF, ePub and Kindle
Exact solutions to Einstein’s equations have been useful for the understanding of general relativity in many respects. They have led to such physical concepts as black holes and event horizons, and helped to visualize interesting features of the theory. This volume studies the solutions to the Ernst equation associated to Riemann surfaces in detail. In addition, the book discusses the physical and mathematical aspects of this class analytically as well as numerically.
Author | : Ray d'Inverno |
Publisher | : Cambridge University Press |
Total Pages | : 402 |
Release | : 1992-12-10 |
Genre | : Mathematics |
ISBN | : 0521439760 |
Download Approaches to Numerical Relativity Book in PDF, ePub and Kindle
Contributions by leading workers in the field given at an international workshop on Numerical Relativity held in Southampton in December 1991.
Author | : Philip Russell Wallace |
Publisher | : Courier Corporation |
Total Pages | : 644 |
Release | : 1984-01-01 |
Genre | : Science |
ISBN | : 0486646769 |
Download Mathematical Analysis of Physical Problems Book in PDF, ePub and Kindle
This mathematical reference for theoretical physics employs common techniques and concepts to link classical and modern physics. It provides the necessary mathematics to solve most of the problems. Topics include the vibrating string, linear vector spaces, the potential equation, problems of diffusion and attenuation, probability and stochastic processes, and much more. 1972 edition.
Author | : Miguel Alcubierre |
Publisher | : OUP Oxford |
Total Pages | : 464 |
Release | : 2008-04-10 |
Genre | : Science |
ISBN | : 0191548294 |
Download Introduction to 3+1 Numerical Relativity Book in PDF, ePub and Kindle
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 | : Carles Bona |
Publisher | : Springer Science & Business Media |
Total Pages | : 226 |
Release | : 2009-07-24 |
Genre | : Science |
ISBN | : 3642011632 |
Download Elements of Numerical Relativity and Relativistic Hydrodynamics Book in PDF, ePub and Kindle
Many large-scale projects for detecting gravitational radiation are currently being developed, all with the aim of opening a new window onto the observable Universe. As a result, numerical relativity has recently become a major field of research, and Elements of Numerical Relativity and Relativistic Hydrodynamics is a valuable primer for both graduate students and non-specialist researchers wishing to enter the field. A revised and significantly enlarged edition of LNP 673 Elements of Numerical Relativity, this book starts with the most basic insights and aspects of numerical relativity before it develops coherent guidelines for the reliable and convenient selection of each of the following key aspects: evolution formalism; gauge, initial, and boundary conditions; and various numerical algorithms. And in addition to many revisions, it includes new, convenient damping terms for numerical implementations, a presentation of the recently-developed harmonic formalism, and an extensive, new chapter on matter space-times, containing a thorough introduction to relativistic hydrodynamics. While proper reference is given to advanced applications requiring large computational resources, most tests and applications in this book can be performed on a standard PC.
Author | : Éric Gourgoulhon |
Publisher | : Springer |
Total Pages | : 304 |
Release | : 2012-02-27 |
Genre | : Science |
ISBN | : 3642245250 |
Download 3+1 Formalism in General Relativity Book in PDF, ePub and Kindle
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.