Download or read book Conformal Methods in General Relativity written by Juan A. Valiente Kroon and published by Cambridge University Press. This book was released on 2023-01-31 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2016 volume, now reissued as OA, shows how conformal methods can be used to study Einstein's theory of gravity.
Download or read book Conformal Methods in General Relativity written by Juan A. Valiente Kroon and published by Cambridge University Press. This book was released on 2016-07-21 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic and self-contained account, which adopts a geometric approach to study the solutions of Einstein's theory of gravity.
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.
Download or read book General Relativity and the Einstein Equations written by Yvonne Choquet-Bruhat and published by Oxford University Press. This book was released on 2009 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.
Download or read book Conformal Field Theory written by Sergei V Ketov and published by World Scientific. This book was released on 1995-02-28 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal field theory is an elegant and powerful theory in the field of high energy physics and statistics. In fact, it can be said to be one of the greatest achievements in the development of this field. Presented in two dimensions, this book is designed for students who already have a basic knowledge of quantum mechanics, field theory and general relativity. The main idea used throughout the book is that conformal symmetry causes both classical and quantum integrability. Instead of concentrating on the numerous applications of the theory, the author puts forward a discussion of the general methods of conformal field theory as a physical theory. Hence the book provides in a self-contained way the necessary knowledge and “conformal” intuition which underline the various applications of conformal field theory. It is aimed to assist students and professionals in the study of the theory from its first principles and in applying the methods in their own research. The first of its kind, this book promises to give a detailed and comprehensive insight into the workings of conformal field theory.
Download or read book General Relativity and Gravitation written by Abhay Ashtekar and published by Cambridge University Press. This book was released on 2015-06-01 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore spectacular advances in cosmology, relativistic astrophysics, gravitational wave science, mathematics, computational science, and the interface of gravitation and quantum physics with this unique celebration of the centennial of Einstein's discovery of general relativity. Twelve comprehensive and in-depth reviews, written by a team of world-leading international experts, together present an up-to-date overview of key topics at the frontiers of these areas, with particular emphasis on the significant developments of the last three decades. Interconnections with other fields of research are also highlighted, making this an invaluable resource for both new and experienced researchers. Commissioned by the International Society on General Relativity and Gravitation, and including accessible introductions to cutting-edge topics, ample references to original research papers, and informative colour figures, this is a definitive reference for researchers and graduate students in cosmology, relativity, and gravitational science.
Download or read book Asymptotic Analysis in General Relativity written by Thierry Daudé and published by Cambridge University Press. This book was released on 2018-01-11 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to modern methods for classical and quantum fields in general relativity / Thierry Daudé, Dietrich Häfner, and Jean-Philippe Nicolas -- Geometry of black hole spacetimes / Lars Andersson, Thomas B. Ackdahl, and Pieter Blue -- An introduction to Quantum Field Theory on curved space-times / Christian Gerard -- A minicourse on microlocal analysis for wave propagation / Andras Vasy -- An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity / Sean N. Curry and A. Rod Gover
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.
Download or read book Techniques of Differential Topology in Relativity written by Roger Penrose and published by SIAM. This book was released on 1972-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.
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.
Download or read book General Relativity and the Einstein Equations written by Yvonne Choquet-Bruhat and published by OUP Oxford. This book was released on 2008-12-04 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Relativity has passed all experimental and observational tests to model the motion of isolated bodies with strong gravitational fields, though the mathematical and numerical study of these motions is still in its infancy. It is believed that General Relativity models our cosmos, with a manifold of dimensions possibly greater than four and debatable topology opening a vast field of investigation for mathematicians and physicists alike. Remarkable conjectures have been proposed, many results have been obtained but many fundamental questions remain open. In this monograph, aimed at researchers in mathematics and physics, the author overviews the basic ideas in General Relativity, introduces the necessary mathematics and discusses some of the key open questions in the field.
Download or read book Noether Symmetries in Theories of Gravity written by Francesco Bajardi and published by Cambridge University Press. This book was released on 2022-11-30 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume summarizes the many modified theories of gravity and shows how to select physically viable models using symmetry principles.
Download or read book The Large Scale Structure of Space Time written by Stephen W. Hawking and published by Cambridge University Press. This book was released on 2023-02-16 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1973, this influential work discusses Einstein's General Theory of Relativity to show how two of its predictions arise: first, that the ultimate fate of many massive stars is to undergo gravitational collapse to form 'black holes'; and second, that there was a singularity in the past at the beginning of the universe. Starting with a precise formulation of the theory, including the necessary differential geometry, the authors discuss the significance of space-time curvature and examine the properties of a number of exact solutions of Einstein's field equations. They develop the theory of the causal structure of a general space-time, and use it to prove a number of theorems establishing the inevitability of singularities under certain conditions. A Foreword contributed by Abhay Ashtekar and a new Preface from George Ellis help put the volume into context of the developments in the field over the past fifty years.
Download or read book Relativistic Fluid Dynamics in and out of Equilibrium written by Paul Romatschke and published by Cambridge University Press. This book was released on 2019-05-09 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a powerful new framework for out-of-equilibrium hydrodynamics, with connections to kinetic theory, AdS/CFT and applications to high-energy particle collisions.
Download or read book Foundations of General Relativity written by Klaas Landsman and published by Radboud University Press. This book was released on 2021-10-08 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, dedicated to Roger Penrose, is a second, mathematically oriented course in general relativity. It contains extensive references and occasional excursions in the history and philosophy of gravity, including a relatively lengthy historical introduction. The book is intended for all students of general relativity of any age and orientation who have a background including at least first courses in special and general relativity, differential geometry, and topology. The material is developed in such a way that through the last two chapters the reader may acquire a taste of the modern mathematical study of black holes initiated by Penrose, Hawking, and others, as further influenced by the initial-value or PDE approach to general relativity. Successful readers might be able to begin reading research papers on black holes, especially in mathematical physics and in the philosophy of physics. The chapters are: Historical introduction, General differential geometry, Metric differential geometry, Curvature, Geodesics and causal structure, The singularity theorems of Hawking and Penrose, The Einstein equations, The 3+1 split of space-time, Black holes I: Exact solutions, and Black holes II: General theory. These are followed by two appendices containing background on Lie groups, Lie algebras, & constant curvature, and on Formal PDE theory.
Download or read book The Theory and Applications of Instanton Calculations written by Manu Paranjape and published by Cambridge University Press. This book was released on 2017-11-16 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Instantons, or pseudoparticles, are solutions to the equations of motion in classical field theories on a Euclidean spacetime. Instantons are found everywhere in quantum theories as they have many applications in quantum tunnelling. Diverse physical phenomena may be described through quantum tunnelling, for example: the Josephson effect, the decay of meta-stable nuclear states, band formation in tight binding models of crystalline solids, the structure of the gauge theory vacuum, confinement in 2+1 dimensions, and the decay of superheated or supercooled phases. Drawing inspiration from Sidney Coleman's Erice lectures, this volume provides an accessible, detailed introduction to instanton methods, with many applications, making it a valuable resource for graduate students in many areas of physics, from condensed matter, particle and nuclear physics, to string theory.
Download or read book Non Inertial Frames and Dirac Observables in Relativity written by Luca Lusanna and published by Cambridge University Press. This book was released on 2019-07-04 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interpreting general relativity relies on a proper description of non-inertial frames and Dirac observables. This book describes global non-inertial frames in special and general relativity. The first part covers special relativity and Minkowski space time, before covering general relativity, globally hyperbolic Einstein space-time, and the application of the 3+1 splitting method to general relativity. The author uses a Hamiltonian description and the Dirac–Bergmann theory of constraints to show that the transition between one non-inertial frame and another is a gauge transformation, extra variables describing the frame are gauge variables, and the measureable matter quantities are gauge invariant Dirac observables. Point particles, fluids and fields are also discussed, including how to treat the problems of relative times in the description of relativistic bound states, and the problem of relativistic centre of mass. Providing a detailed description of mathematical methods, the book is perfect for theoretical physicists, researchers and students working in special and general relativity.
