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The Einstein Equations And The Large Scale Behavior Of Gravitational Fields
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Book Synopsis The Einstein Equations and the Large Scale Behavior of Gravitational Fields by : Piotr T. Chrusciel
Download or read book The Einstein Equations and the Large Scale Behavior of Gravitational Fields written by Piotr T. Chrusciel and published by Birkhäuser. This book was released on 2012-12-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.
Book Synopsis Philosophy of Physics by : Jeremy Butterfield
Download or read book Philosophy of Physics written by Jeremy Butterfield and published by Elsevier. This book was released on 2007 with total page 1481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ambition of this volume is twofold: to provide a comprehensive overview of the field and to serve as an indispensable reference work for anyone who wants to work in it. For example, any philosopher who hopes to make a contribution to the topic of the classical-quantum correspondence will have to begin by consulting Klaas Landsman's chapter. The organization of this volume, as well as the choice of topics, is based on the conviction that the important problems in the philosophy of physics arise from studying the foundations of the fundamental theories of physics. It follows that there is no sharp line to be drawn between philosophy of physics and physics itself. Some of the best work in the philosophy of physics is being done by physicists, as witnessed by the fact that several of the contributors to the volume are theoretical physicists: viz., Ellis, Emch, Harvey, Landsman, Rovelli, 't Hooft, the last of whom is a Nobel laureate. Key features - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers - Definitive discussions of the philosophical implications of modern physics - Masterly expositions of the fundamental theories of modern physics - Covers all three main pillars of modern physics: relativity theory, quantum theory, and thermal physics - Covers the new sciences that have grown from these theories: for example, cosmology from relativity theory; and quantum information and quantum computing, from quantum theory - Contains special Chapters that address crucial topics that arise in several different theories, such as symmetry and determinism - Written by very distinguished theoretical physicists, including a Nobel Laureate, as well as by philosophers
Book Synopsis General Relativity by : Prakash Borah
Download or read book General Relativity written by Prakash Borah and published by BookRix. This book was released on 2023-08-15 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of General Relativity, formulated by Albert Einstein in 1915, revolutionized our understanding of gravity and the nature of spacetime. This theory proposes that gravity is not a force transmitted between masses, but rather a curvature of spacetime caused by mass and energy. In this abstract, we provide a concise overview of the key principles and implications of General Relativity. We discuss the equivalence principle, which states that inertial and gravitational mass are indistinguishable, leading to the geodesic motion of particles in curved spacetime. The Einstein field equations, a set of nonlinear differential equations, describe how matter and energy distribution determine the curvature of spacetime. These equations predict the behavior of gravitational waves, the bending of light in a gravitational field (gravitational lensing), and the existence of black holes. General Relativity has been confirmed through various experiments and observations, including the deflection of starlight during a solar eclipse and the recent detection of gravitational waves. Its profound influence on cosmology and our understanding of the universe's large-scale structure continues to drive scientific inquiry and shape our comprehension of fundamental physics.
Book Synopsis General Relativity and the Einstein Equations by : Yvonne Choquet-Bruhat
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 General Relativistic Dynamics written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis General Relativistic Dynamics by : Fred I. Cooperstock
Download or read book General Relativistic Dynamics written by Fred I. Cooperstock and published by World Scientific. This book was released on 2009 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings Einstein's general relativity into action in new ways at scales ranging from the tiny Planck scale to the scale of immense galactic clusters. It presents the case that Einstein's theory of gravity can describe the observed dynamics of galaxies without invoking the unknown OC dark matterOCO required in models based on Newtonian gravity. Drawing on the author's experience as a lecturer and on his own research, the book covers the essentials of Einstein's special and general relativity at a level accessible to undergraduate students. The early chapters provide a compact introduction to relativity for readers who have little or no background in the subject. Hermann Bondi's very transparent approach to special relativity is expanded to resolve the OC twin paradoxOCO using only elementary mathematics. In later chapters, general relativity is used to extend the concept of the Planck scale, to address the role of the cosmological term and to analyze the concept of OC time machinesOCO.
Book Synopsis Einstein Equations: Physical and Mathematical Aspects of General Relativity by : Sergio Cacciatori
Download or read book Einstein Equations: Physical and Mathematical Aspects of General Relativity written by Sergio Cacciatori and published by Springer Nature. This book was released on 2019-11-23 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at the first edition of the Domoschool, the International Alpine School in Mathematics and Physics, held in Domodossola, Italy, in July 2018. It is divided into two parts. Part I consists of four sets of lecture notes. These are extended versions of lectures given at the Domoschool, written by well-known experts in mathematics and physics related to General Relativity. Part II collects talks by selected participants, focusing on research related to General Relativity.
Book Synopsis Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity by : Sergio Luigi Cacciatori
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.
Book Synopsis On the Topology and Future Stability of the Universe by : Hans Ringström
Download or read book On the Topology and Future Stability of the Universe written by Hans Ringström and published by OUP Oxford. This book was released on 2013-05-23 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: The standard starting point in cosmology is the cosmological principle; the assumption that the universe is spatially homogeneous and isotropic. After imposing this assumption, the only freedom left, as far as the geometry is concerned, is the choice of one out of three permissible spatial geometries, and one scalar function of time. Combining the cosmological principle with an appropriate description of the matter leads to the standard models. It is worth noting that these models yield quite a successful description of our universe. However, even though the universe may, or may not, be almost spatially homogeneous and isotropic, it is clear that the cosmological principle is not exactly satisfied. This leads to several questions. The most natural one concerns stability: given initial data corresponding to an expanding model of the standard type, do small perturbations give rise to solutions that are similar to the future? Another question concerns the shape of the universe: what are the restrictions if we only assume the universe to appear almost spatially homogeneous and isotropic to every observer? The main purpose of the book is to address these questions. However, to begin with, it is necessary to develop the general theory of the Cauchy problem for the Einstein-Vlasov equations. In order to to make the results accessible to researchers who are not mathematicians, but who are familiar with general relativity, the book contains an extensive prologue putting the results into a more general context.
Book Synopsis Stability by Linearization of Einstein's Field Equation by : Lluís Bruna
Download or read book Stability by Linearization of Einstein's Field Equation written by Lluís Bruna and published by Springer Science & Business Media. This book was released on 2013-11-25 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: V ? V ?K? , 3 2 2 R ? /?x K i i g V T G g ?T , ? G g g 4 ? R ? ? G ? T g g ? h h ? 2 2 2 2 ? ? ? ? ? ? ? h ?S , ?? ?? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 S T S T? T?. ? ̃ T S 2 2 2 2 ? ? ? ? ? ? ? h . ?? 2 2 2 2 2 c ?t ?x ?x ?x 1 2 3 g h h ?? g T T g vacuum M n R n R Acknowledgements n R Chapter I Pseudo-Riemannian Manifolds I.1 Connections M C n X M C M F M C X M F M connection covariant derivative M ? X M ×X M ?? X M X,Y ?? Y X ? Y ? Y ? Y X +X X X 1 2 1 2 ? Y Y ? Y ? Y X 1 2 X 1 X 2 ? Y f? Y f?F M fX X ? fY X f Y f? Y f?F M X X ? torsion ? Y?? X X,Y X,Y?X M . X Y localization principle Theorem I.1. Let X, Y, X , Y be C vector ?elds on M.Let U be an open set
Book Synopsis Numerical Relativity by : Thomas W. Baumgarte
Download or read book Numerical Relativity written by Thomas W. Baumgarte and published by Cambridge University Press. This book was released on 2010-06-24 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pedagogical introduction to numerical relativity for students and researchers entering the field, and interested scientists.
Book Synopsis General Relativity and Gravitation by : Abhay Ashtekar
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.
Book Synopsis Relativity and Gravitation by : Jiří Bičák
Download or read book Relativity and Gravitation written by Jiří Bičák and published by Springer. This book was released on 2014-06-06 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: In early April 1911 Albert Einstein arrived in Prague to become full professor of theoretical physics at the German part of Charles University. It was there, for the first time, that he concentrated primarily on the problem of gravitation. Before he left Prague in July 1912 he had submitted the paper “Relativität und Gravitation: Erwiderung auf eine Bemerkung von M. Abraham” in which he remarkably anticipated what a future theory of gravity should look like. At the occasion of the Einstein-in-Prague centenary an international meeting was organized under a title inspired by Einstein's last paper from the Prague period: "Relativity and Gravitation, 100 Years after Einstein in Prague". The main topics of the conference included: classical relativity, numerical relativity, relativistic astrophysics and cosmology, quantum gravity, experimental aspects of gravitation and conceptual and historical issues. The conference attracted over 200 scientists from 31 countries, among them a number of leading experts in the field of general relativity and its applications. This volume includes abstracts of the plenary talks and full texts of contributed talks and articles based on the posters presented at the conference. These describe primarily original results of the authors. Full texts of the plenary talks are included in the volume "General Relativity, Cosmology and Astrophysics--Perspectives 100 Years after Einstein in Prague", eds. J. Bičák and T. Ledvinka, published also by Springer Verlag.
Book Synopsis The Oxford Handbook of Philosophy of Physics by : Robert Batterman
Download or read book The Oxford Handbook of Philosophy of Physics written by Robert Batterman and published by Oxford University Press. This book was released on 2013-01-04 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Oxford Handbook provides an overview of many of the topics that currently engage philosophers of physics. It surveys new issues and the problems that have become a focus of attention in recent years. It also provides up-to-date discussions of the still very important problems that dominated the field in the past. In the late 20th Century, the philosophy of physics was largely focused on orthodox Quantum Mechanics and Relativity Theory. The measurement problem, the question of the possibility of hidden variables, and the nature of quantum locality dominated the literature on the quantum mechanics, whereas questions about relationalism vs. substantivalism, and issues about underdetermination of theories dominated the literature on spacetime. These issues still receive considerable attention from philosophers, but many have shifted their attentions to other questions related to quantum mechanics and to spacetime theories. Quantum field theory has become a major focus, particularly from the point of view of algebraic foundations. Concurrent with these trends, there has been a focus on understanding gauge invariance and symmetries. The philosophy of physics has evolved even further in recent years with attention being paid to theories that, for the most part, were largely ignored in the past. For example, the relationship between thermodynamics and statistical mechanics---once thought to be a paradigm instance of unproblematic theory reduction---is now a hotly debated topic. The implicit, and sometimes explicit, reductionist methodology of both philosophers and physicists has been severely criticized and attention has now turned to the explanatory and descriptive roles of "non-fundamental,'' phenomenological theories. This shift of attention includes "old'' theories such as classical mechanics, once deemed to be of little philosophical interest. Furthermore, some philosophers have become more interested in "less fundamental'' contemporary physics such as condensed matter theory. Questions abound with implications for the nature of models, idealizations, and explanation in physics. This Handbook showcases all these aspects of this complex and dynamic discipline.
Book Synopsis The Large Scale Structure of Space-Time by : S. W. Hawking
Download or read book The Large Scale Structure of Space-Time written by S. W. Hawking and published by Cambridge University Press. This book was released on 1975-02-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
Book Synopsis Quantum Field Theory III: Gauge Theory by : Eberhard Zeidler
Download or read book Quantum Field Theory III: Gauge Theory written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2011-08-17 with total page 1141 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).
Book Synopsis Geometric Analysis Around Scalar Curvatures by : Fei Han
Download or read book Geometric Analysis Around Scalar Curvatures written by Fei Han and published by World Scientific. This book was released on 2016-04-18 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains three expanded lecture notes from the program Scalar Curvature in Manifold Topology and Conformal Geometry that was held at the Institute for Mathematical Sciences from 1 November to 31 December 2014. The first chapter surveys the recent developments on the fourth-order equations with negative exponent from geometric points of view such as positive mass theorem and uniqueness results. The next chapter deals with the recent important progress on several conjectures such as the existence of non-flat smooth hyper-surfaces and Serrin's over-determined problem. And the final chapter induces a new technique to handle the equation with critical index and the sign change coefficient as well as the negative index term. These topics will be of interest to those studying conformal geometry and geometric partial differential equations. Contents:Lectures on the Fourth-Order Q Curvature Equation (Fengbo Hang and Paul C Yang)An Introduction to the Finite and Infinite Dimensional Reduction Methods (Manuel del Pino and Juncheng Wei)Einstein Constraint Equations on Riemannian Manifolds (Quôc Anh Ngô) Readership: Advanced undergraduates, graduate students and researchers interested in the study of conformal geometry and geometric partial differential equations.
