Applicability of Fluid Dynamics in General Relativity PDF Download
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Author: Aziz Khan Jahja
Publisher:
ISBN:
Category :
Languages : en
Pages : 108
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Book Description
Author: Aziz Khan Jahja
Publisher:
ISBN:
Category :
Languages : en
Pages : 108
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Book Description
Author: Harish Parthasarathy
Publisher: CRC Press
ISBN: 1000387658
Category : Science
Languages : en
Pages : 691
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Book Description
This is a reference book for researchers working in the field of general relativity, quantum mechanics and quantum gravity. A major part of the book deals with the formulation of special relativistic mechanics, special relativistic fluid dynamics and its generalization to general relativity where the gravitational field is described by a metric tensor. Emphasis is laid on the fact that the general theory of relativity is of tensorial character under all dieomorphisms of space-time and hence its field equations, namely the Einstein field equations for gravitation, the Maxwell equations in a curved space-time geometry and the fluid dynamical equations in curved space time are all valid for all observers in the universe. The emphasis throughout is on the fact that matter generates a gravitational field described by a metric that has a non-vanishing curvature tensor and hence such space-times are inherently curved, ie, cannot be transformed into Minkowsian form. There is a final section on quantum mechanics and quantum field theory which introduces supersymmetry and quantum gravity to the reader. The reader after going through this book will be sufficiently well equipped to start research in quantum gravity, i.e, background independent physics which is as yet an unsolved problem owing to renormalization problems. Note: T& F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.
Author: Demetrios Christodoulou
Publisher: European Mathematical Society
ISBN: 9783037190050
Category : Science
Languages : en
Pages : 164
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Book Description
General relativity is a theory proposed by Einstein in 1915 as a unified theory of space, time and gravitation. It is based on and extends Newton's theory of gravitation as well as Newton's equations of motion. It is thus fundamentally rooted in classical mechanics. The theory can be seen as a development of Riemannian geometry, itself an extension of Gauss' intrinsic theory of curved surfaces in Euclidean space. The domain of application of the theory is astronomical systems. One of the mathematical methods analyzed and exploited in the present volume is an extension of Noether's fundamental principle connecting symmetries to conserved quantities. This is involved at a most elementary level in the very definition of the notion of hyperbolicity for an Euler-Lagrange system of partial differential equations. Another method, the study and systematic use of foliations by characteristic (null) hypersurfaces, is in the spirit of Roger Penrose's approach in his incompleteness theorem. The methods have applications beyond general relativity to problems in fluid mechanics and, more generally, to the mechanics and electrodynamics of continuous media. The book is intended for advanced students and researchers seeking an introduction to the methods and applications of general relativity.
Author: A. M. Anile
Publisher: Cambridge University Press
ISBN: 9780521304061
Category : Science
Languages : en
Pages : 352
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Book Description
A unified and systematic treatment of the main results and techniques of relativistic fluid dynamics with an emphasis on waves and shock waves. The first four chapters provide an introduction to the fundamental principles of relativistic fluid dynamics and magneto-fluids. The remaining chapters present specific topics, including non-linear electromagnetic waves in relativistic cold plasmas, relativistic asymptotic waves, and relativistic shock waves. Examples of the applications of the theory to plasma physics, nuclear physics and astrophysics are presented.
Author: Nikolaos Athanasiou
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Paul Romatschke
Publisher: Cambridge University Press
ISBN: 1108483682
Category : Science
Languages : en
Pages : 207
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Book Description
Presents a powerful new framework for out-of-equilibrium hydrodynamics, with connections to kinetic theory, AdS/CFT and applications to high-energy particle collisions.
Author: C. Cattaneo
Publisher: Springer Science & Business Media
ISBN: 3642110991
Category : Mathematics
Languages : en
Pages : 420
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Book Description
Pham Mau Quam: Problèmes mathématiques en hydrodynamique relativiste.- A. Lichnerowicz: Ondes de choc, ondes infinitésimales et rayons en hydrodynamique et magnétohydrodynamique relativistes.- A.H. Taub: Variational principles in general relativity.- J. Ehlers: General relativistic kinetic theory of gases.- K. Marathe: Abstract Minkowski spaces as fibre bundles.- G. Boillat: Sur la propagation de la chaleur en relativité.
Author: Luciano Rezzolla
Publisher: OUP Oxford
ISBN: 0191509914
Category : Science
Languages : en
Pages : 752
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Book Description
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solution of the equations, and over to the applications in modern physics and astrophysics. Numerous figures, diagrams, and a variety of exercises aid the material in the book. The most obvious applications of this work range from astrophysics (black holes, neutron stars, gamma-ray bursts, and active galaxies) to cosmology (early-universe hydrodynamics and phase transitions) and particle physics (heavy-ion collisions). It is often said that fluids are either seen as solutions of partial differential equations or as "wet". Fluids in this book are definitely wet, but the mathematical beauty of differential equations is not washed out.
Author: Carles Bona
Publisher: Springer
ISBN: 3642011640
Category : Science
Languages : en
Pages : 226
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Book Description
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: A. M. Anile
Publisher: Cambridge University Press
ISBN: 9780521018128
Category : Science
Languages : en
Pages : 352
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Book Description
A unified and systematic treatment of the main results and techniques of relativistic fluid dynamics with an emphasis on waves and shock waves. The first four chapters provide an introduction to the fundamental principles of relativistic fluid dynamics and magneto-fluids. The remaining chapters present specific topics, including non-linear electromagnetic waves in relativistic cold plasmas, relativistic asymptotic waves, and relativistic shock waves. Examples of the applications of the theory to plasma physics, nuclear physics and astrophysics are presented.
