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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.
Einstein field equations --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Differential equations --- Field theory (Physics) --- General relativity (Physics) --- Gravitational fields --- Gravitation. --- Mathematical physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Mathematical Physics. --- Physical mathematics --- Physics --- Matter --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Mathematics --- Properties
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This collection of papers presents ideas and problems arising over the past 100 years regarding classical and quantum gravity, gauge theories of gravity, and spacetime transformations of accelerated frames. Both Einstein's theory of gravity and the Yang-Mills theory are gauge invariant. The invariance principles in physics have transcended both kinetic and dynamic properties and are at the very heart of our understanding of the physical world. In this spirit, this book attempts to survey the development of various formulations for gravitational and Yang-Mills fields and spacetime transformatio
Gravitation. --- Relativity (Physics) --- Einstein field equations. --- Yang-Mills theory. --- Mills-Yang theory --- Yang-Mills theories --- Quantum field theory --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Differential equations --- Field theory (Physics) --- General relativity (Physics) --- Gravitational fields --- Gravitation --- Nonrelativistic quantum mechanics --- Space and time --- Matter --- Physics --- Antigravity --- Centrifugal force --- Properties
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As the structures in our Universe are mapped out on ever larger scales, and with increasing detail, the use of inhomogeneous models is becoming an essential tool for analyzing and understanding them. This book reviews a number of important developments in the application of inhomogeneous solutions of Einstein's field equations to cosmology. It shows how inhomogeneous models can be employed to study the evolution of structures such as galaxy clusters and galaxies with central black holes, and to account for cosmological observations like supernovae dimming, the cosmic microwave background, baryon acoustic oscillations or the dependence of the Hubble parameter on redshift within classical general relativity. Whatever `dark matter' and `dark energy' turn out to be, inhomogeneities exist on many scales and need to be investigated with all appropriate methods. This book is of great value to all astrophysicists and researchers working in cosmology, from graduate students to academic researchers.
Cosmology --- Einstein field equations. --- Inhomogeneous materials. --- Heterogeneous materials --- Inhomogeneous media --- Media, Inhomogeneous --- Materials --- Matter --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Differential equations --- Field theory (Physics) --- General relativity (Physics) --- Gravitational fields --- Astronomy --- Deism --- Metaphysics --- Mathematics.
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Quantum gravity. --- Einstein field equations. --- Dark matter (Astronomy) --- General relativity (Physics) --- Gravity, Quantum --- Gravitation --- Quantum theory --- Relativistic theory of gravitation --- Relativity theory, General --- Physics --- Relativity (Physics) --- Nonluminous matter (Astronomy) --- Unobserved matter (Astronomy) --- Unseen matter (Astronomy) --- Interstellar matter --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Differential equations --- Field theory (Physics) --- Gravitational fields
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A brief introduction to gravity through Einstein's general theory of relativityOf the four fundamental forces of nature, gravity might be the least understood and yet the one with which we are most intimate. From the months each of us spent suspended in the womb anticipating birth to the moments when we wait for sleep to transport us to other realities, we are always aware of gravity. In On Gravity, physicist A. Zee combines profound depth with incisive accessibility to take us on an original and compelling tour of Einstein's general theory of relativity. Inspired by Einstein's audacious suggestion that spacetime could ripple, Zee begins with the stunning discovery of gravity waves. He goes on to explain how gravity can be understood in comparison to other classical field theories, presents the idea of curved spacetime and the action principle, and explores cutting-edge topics, including black holes and Hawking radiation. Zee travels as far as the theory reaches, leaving us with tantalizing hints of the utterly unknown, from the intransigence of quantum gravity to the mysteries of dark matter and energy.Concise and precise, and infused with Zee's signature warmth and freshness of style, On Gravity opens a unique pathway to comprehending relativity and gaining deep insight into gravity, spacetime, and the workings of the universe.
Einstein field equations. --- General relativity (Physics) --- Gravity. --- Relativity (Physics) --- SCIENCE / Gravity. --- Gravitation --- Nonrelativistic quantum mechanics --- Space and time --- Geophysics --- Mechanics --- Pendulum --- Relativistic theory of gravitation --- Relativity theory, General --- Physics --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Differential equations --- Field theory (Physics) --- Gravitational fields
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This book attempts to eliminate the existing “imbalance” between the theory of electric machines and the theory of electromagnetic fields. In order to develop viable methods for engineering calculations, the author applies field equations. The resulting, new methods consist of traditional calculation elements represented in a refined form (circuit-loops, parameters, equivalent circuits and voltage equations). These calculation methods should be effective both for researchers and engineering practitioners, especially, in relation to the modern electric machines, such as powerful turbine generators, large high-speed synchronous motors, etc. Provides conditions for the generalization of the field research results; Expands capabilities of engineering calculation methods; Improves upon the theory of engineering calculations, under the conditions of the Maxwell’s equations.
Einstein field equations. --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Differential equations --- Field theory (Physics) --- General relativity (Physics) --- Gravitational fields --- Power electronics. --- Electric machinery. --- Electronic circuits. --- Power Electronics. --- Electrical Machines. --- Electronic Circuits and Systems. --- Electron-tube circuits --- Electric circuits --- Electron tubes --- Electronics --- Electromechanical devices --- Machinery --- Electronics, Power --- Electric power
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This monograph presents a self contained mathematical treatment of the initial value problem for shock wave solutions of the Einstein equations in General Relativity. The first two chapters provide background for the introduction of a locally intertial Glimm Scheme, a non-dissipative numerical scheme for approximating shock wave solutions of the Einstein equations in spherically symmetric spacetimes. What follows is a careful analysis of this scheme providing a proof of the existence of (shock wave) solutions of the spherically symmetric Einstein equations for a perfect fluid, starting from initial density and velocity profiles that are only locally of bounded total variation. The book covers the initial value problems for Einstein's gravitational field equations with fluid sources and shock wave initial data. It has a clearly outlined goal: proving a certain local existence theorem. Concluding remarks are added and commentary is provided throughout. The book will be useful to graduate students and researchers in mathematics and physics.
Einstein field equations. --- Shock waves. --- Shock (Mechanics) --- Waves --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Differential equations --- Field theory (Physics) --- General relativity (Physics) --- Gravitational fields --- Mathematics. --- Applications of Mathematics. --- Classical and Quantum Gravitation, Relativity Theory. --- Math --- Science --- Applied mathematics. --- Engineering mathematics. --- Gravitation. --- Engineering --- Engineering analysis --- Mathematical analysis --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Mathematics --- Properties
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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.
General relativity (Physics) --- Einstein field equations --- Numerical calculations --- 530.12 --- Relativity principle --- Einstein field equations. --- Numerical calculations. --- General relativity (Physics). --- 530.12 Relativity principle --- Numerical analysis --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics --- Relativity (Physics) --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Differential equations --- Field theory (Physics) --- Gravitational fields --- Nonrelativistic quantum mechanics --- Space and time --- Computer programs. --- Data processing.
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Quantum mechanics. Quantumfield theory --- Differential equations --- Mathematical physics --- Einstein field equations. --- Shock waves --- Relativistic quantum theory. --- General relativity (Physics) --- Equations du champ d'Einstein --- Ondes de choc --- Théorie quantique relativiste --- Relativité générale (Physique) --- Mathematical models --- Modèles mathématiques --- Mathematical models. --- 51 <082.1> --- Mathematics--Series --- Shock waves. --- Théorie quantique relativiste --- Relativité générale (Physique) --- Modèles mathématiques --- Einstein field equations --- Relativistic quantum theory --- Shock (Mechanics) --- Waves --- Relativistic quantum mechanics --- Quantum theory --- Special relativity (Physics) --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics --- Relativity (Physics) --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Field theory (Physics) --- Gravitational fields
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Partial differential equations --- 514.8 --- Geometric study of objects of mechanics and physics --- 514.8 Geometric study of objects of mechanics and physics --- Conservation laws (Physics) --- Einstein field equations. --- Shock waves. --- Singularities (Mathematics) --- General relativity (Physics) --- Lois de conservation (physique) --- Einstein, Équations du champ d' --- Ondes de choc --- Singularités (mathématiques) --- Relativité générale (physique) --- Einstein field equations --- Shock waves --- Geometry, Algebraic --- Shock (Mechanics) --- Waves --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics --- Relativity (Physics) --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Differential equations --- Field theory (Physics) --- Gravitational fields --- Physical laws --- Einstein, Équations du champ d'. --- Ondes de choc.
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