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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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Since Einstein first described them nearly a century ago, gravitational waves have been the subject of more sustained controversy than perhaps any other phenomenon in physics. These as yet undetected fluctuations in the shape of space-time were first predicted by Einstein's general theory of relativity, but only now, at the dawn of the twenty-first century, are we on the brink of finally observing them. Daniel Kennefick's landmark book takes readers through the theoretical controversies and thorny debates that raged around the subject of gravitational waves after the publication of Einstein's theory. The previously untold story of how we arrived at a settled theory of gravitational waves includes a stellar cast from the front ranks of twentieth-century physics, including Richard Feynman, Hermann Bondi, John Wheeler, Kip Thorne, and Einstein himself, who on two occasions avowed that gravitational waves do not exist, changing his mind both times. The book derives its title from a famously skeptical comment made by Arthur Stanley Eddington in 1922--namely, that "gravitational waves propagate at the speed of thought." Kennefick uses the title metaphorically to contrast the individual brilliance of each of the physicists grappling with gravitational-wave theory against the frustratingly slow progression of the field as a whole. Accessibly written and impeccably researched, this book sheds new light on the trials and conflicts that have led to the extraordinary position in which we find ourselves today--poised to bring the story of gravitational waves full circle by directly confirming their existence for the very first time.

Space and time. --- General relativity (Physics) --- Einstein field equations. --- Gravitational waves. --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Fourth dimension --- Infinite --- Metaphysics --- Philosophy --- Space sciences --- Time --- Beginning --- Hyperspace --- Relativity (Physics) --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- 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 --- Gravitational radiation --- Gravity waves (Astrophysics) --- Radiation --- Waves --- Einstein field equations --- Gravitational waves --- Space and time --- 531.5 --- 531.5 Gravity. Gravitation. Pendulums. Ballistics --- Gravity. Gravitation. Pendulums. Ballistics

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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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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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Spurred by the current development of numerous large-scale projects for detecting gravitational radiation, with the aim to open a completely new window to the observable Universe, numerical relativity has become a major field of research over the past years. Indeed, numerical relativity is the standard approach when studying potential sources of gravitational waves, where strong fields and relativistic velocities are part of any physical scenario. This book can be considered a primer for both graduate students and non-specialist researchers wishing to enter the field. Starting from the most basic insights and aspects of numerical relativity, Elements of Numerical Relativity develops coherent guidelines for the reliable and convenient selection of each of the following key aspects: evolution formalism, gauge, initial and boundary conditions as well as various numerical algorithms. The tests and applications proposed in this book can be performed on a standard PC.

Relativity (Physics) --- Space and time --- Evolution equations --- Einstein field equations --- Relativité (Physique) --- Espace et temps --- Equations d'évolution --- Mathematics. --- Numerical solutions. --- Mathématiques --- Solutions numériques --- Physics. --- Computer science. --- Mathematical physics. --- Relativity (Physics). --- Mathematical and Computational Physics. --- Relativity and Cosmology. --- Computational Science and Engineering. --- Applied Physics --- Physics - General --- Physics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Mathematics --- Numerical solutions --- Einstein's field equations --- Einstein's gravitational field equations --- Einstein's law of gravitation --- Field equations, Einstein --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Physical mathematics --- Informatics --- Natural philosophy --- Philosophy, Natural --- Computer mathematics. --- Gravitation. --- Theoretical, Mathematical and Computational Physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Science --- Computer mathematics --- Electronic data processing --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Properties --- Space and time - Mathematics --- Evolution equations - Numerical solutions --- Einstein field equations - Numerical solutions