Download or read book The Cauchy Problem in General Relativity written by Hans Ringström and published by European Mathematical Society. This book was released on 2009 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theory of relativity is a theory of manifolds equipped with Lorentz metrics and fields which describe the matter content. Einstein's equations equate the Einstein tensor (a curvature quantity associated with the Lorentz metric) with the stress energy tensor (an object constructed using the matter fields). In addition, there are equations describing the evolution of the matter. Using symmetry as a guiding principle, one is naturally led to the Schwarzschild and Friedmann-Lemaitre-Robertson-Walker solutions, modelling an isolated system and the entire universe respectively. In a different approach, formulating Einstein's equations as an initial value problem allows a closer study of their solutions. This book first provides a definition of the concept of initial data and a proof of the correspondence between initial data and development. It turns out that some initial data allow non-isometric maximal developments, complicating the uniqueness issue. The second half of the book is concerned with this and related problems, such as strong cosmic censorship. The book presents complete proofs of several classical results that play a central role in mathematical relativity but are not easily accessible to those without prior background in the subject. Prerequisites are a good knowledge of basic measure and integration theory as well as the fundamentals of Lorentz geometry. The necessary background from the theory of partial differential equations and Lorentz geometry is included.

Download or read book Gravitoelectromagnetism and the Cauchy Problem in General Relativity written by Mark Andrew Spanier Aarons and published by . This book was released on 2000 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book CAUCHY PROBLEM IN GENERAL RELATIVITY written by HANS RINGSTROM. and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Global Aspects of the Cauchy Problem in General Relativity written by Yvonne Choquet-Bruhat and published by . This book was released on 1969 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book General Relativity And Gravitation Proceedings Of The 14th International Conference written by Mauro Francaviglia and published by World Scientific. This book was released on 1997-04-01 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers topics ranging from the early universe, cosmology, inflation, quantum gravity, exact solutions and computer-aided computations to space and terrestrial gravity experiments, with special emphasis on recent research.

Download or read book Notes on a Formulation of the Problem of Initial Conditions in the Cauchy Problem of General Relativity written by Elliot Paul Belasco and published by . This book was released on 1967 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Problems of General Relativity I written by Demetrios Christodoulou and published by European Mathematical Society. This book was released on 2008 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Recent Advances in General Relativity written by Allen I. Janis and published by Springer Science & Business Media. This book was released on 1992-02-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from the Discussion Conference on Recent Advances in General Relativity, held at the U. of Pittsburgh, May 1990, survey the interacting fields of classical general relativity, astrophysics, and quantum gravity. Some of the remarks made following the invited papers are also included. The conference also included three workshops on classical g

Download or read book Introduction to General Relativity Black Holes and Cosmology written by Yvonne Choquet-Bruhat and published by Oxford University Press. This book was released on 2015 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics. Based on Yvonne Choquet-Bruhat's more advanced text, General Relativity and the Einstein Equations, the aim of this book is to give with precision, but as simply as possible, the foundations and main consequences of General Relativity. The first five chapters from General Relativity and the Einstein Equations have been updated with new sections and chapters on black holes, gravitational waves, singularities, and the Reissner-Nordstrom and interior Schwarzchild solutions. The rigour behind this book will provide readers with the perfect preparation to follow the great mathematical progress in the actual development, as well as the ability to model, the latest astrophysical and cosmological observations. The book presents basic General Relativity and provides a basis for understanding and using the fundamental theory.

Download or read book Constraint Damping in the Cauchy Problem in General Relativity written by Allen Juntao Fang and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cauchy Problem in General Relativity is an area of active research in partial differential equations (PDEs). Much progress has been made on the Cauchy Problem in General Relativity via the local existence theory of symmetric hyperbolic systems and the choice of generalized harmonic gauge. The choice of generalized harmonic gauge also allows for the introduction of constraint damping terms, which allow for control over any violation of the general harmonic gauge constraint. In this thesis, we first go through the symmetric hyperbolic theory of partial differential equations since it will establish the basis for our local existence result for Einstein's vacuum equations. Afterwards, we look at the 3+1 formalism as well as generalized harmonic coordinates, before finally proving stability for the damped constraint evolution equations in Minkowski space.

Download or read book General Relativity and Gravitation written by M. A. H. MacCallum and published by CUP Archive. This book was released on 1987-09-24 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Exterior Cauchy Problem of the General Theory of Relativity written by T.G. Berry and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Einstein Equations Local Energy Self Force and Fields in General Relativity written by Sergio Luigi Cacciatori and published by Springer Nature. This book was released on 2023-03-15 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume guides early-career researchers through recent breakthroughs in mathematics and physics as related to general relativity. Chapters are based on courses and lectures given at the July 2019 Domoschool, International Alpine School in Mathematics and Physics, held in Domodossola, Italy, which was titled “Einstein Equations: Physical and Mathematical Aspects of General Relativity”. Structured in two parts, the first features four courses from prominent experts on topics such as local energy in general relativity, geometry and analysis in black hole spacetimes, and antimatter gravity. The second part features a variety of papers based on talks given at the summer school, including topics like: Quantum ergosphere General relativistic Poynting-Robertson effect modelling Numerical relativity Length-contraction in curved spacetime Classicality from an inhomogeneous universe Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity will be a valuable resource for students and researchers in mathematics and physicists interested in exploring how their disciplines connect to general relativity.

Download or read book Lectures on General Relativity Theory written by Alfred Schild and published by . This book was released on 1965 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Cauchy Problem for the Linearised Einstein Equation and the Goursat Problem for Wave Equations written by Oliver Lindblad Petersen and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study two initial value problems arising in general relativity. The first is the Cauchy problem for the linearised Einstein equation on general globally hyperbolic spacetimes, with smooth and distributional initial data. We extend well-known results by showing that given a solution to the linearised constraint equations of arbitrary real Sobolev regularity, there is a globally defined solution, which is unique up to addition of gauge solutions. Two solutions are considered equivalent if they differ by a gauge solution. Our main result is that the equivalence class of solutions depends continuously on the corre- sponding equivalence class of initial data. We also solve the linearised constraint equations in certain cases and show that there exist arbitrarily irregular (non-gauge) solutions to the linearised Einstein equation on Minkowski spacetime and Kasner spacetime. In the second part, we study the Goursat problem (the characteristic Cauchy problem) for wave equations. We specify initial data on a smooth compact ...

Download or read book One Hundred Years of General Relativity written by Shing-Tung Yau and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Physical and Mathematical Foundations of the Theory of Relativity written by Antonio Romano and published by Springer Nature. This book was released on 2019-09-25 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications. The transitions from classical mechanics to special relativity and then to general relativity are explored in detail as well, helping readers to gain a more profound and nuanced understanding of the theory as a whole. After reviewing the fundamentals of differential geometry and classical mechanics, the text introduces special relativity, first using the physical approach proposed by Einstein and then via Minkowski’s mathematical model. The authors then address the relativistic thermodynamics of continua and electromagnetic fields in matter – topics which are normally covered only very briefly in other treatments – in the next two chapters. The text then turns to a discussion of general relativity by means of the authors’ unique critical approach, underlining the difficulty of recognizing the physical meaning of some statements, such as the physical meaning of coordinates and the derivation of physical quantities from those of space-time. Chapters in this section cover the model of space-time proposed by Schwarzschild; black holes; the Friedman equations and the different cosmological models they describe; and the Fermi-Walker derivative. Well-suited for graduate students in physics and mathematics who have a strong foundation in real analysis, classical mechanics, and general physics, this textbook is appropriate for a variety of graduate-level courses that cover topics in relativity. Additionally, it will interest physicists and other researchers who wish to further study the subtleties of these theories and understand the contemporary scholarly discussions surrounding them.