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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.
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In diesem einzigartigen Lehrbuch werden anhand von Anwendungsbeispielen die Grundkonzepte der Mechanik vorgestellt. Es setzt nur wenige mathematische Vorkenntnisse voraus. Insbesondere für Lehramtskandidaten geeignet. Mit zahlreichen farbigen grafischen Illustrationen. Mit vielen Anwendungsbeispielen wie Raketenstart, Bungee-Sprung, Fallschirmsprung aus 30.000 Meter Höhe, Weitsprung, Fahrzeug-Crash, Gezeitenkräfte etc.
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The 16th conference of the International Society on General Relativity and Gravitation (GR16), held at the International Convention Centre in Durban, South Africa, from 15 to 21 July, was attended by 450 delegates from around the world. The scientific programme comprised 18 plenary lectures, 1 public lecture and 19 workshops which, excepting 3 plenary lectures, are presented in this proceedings. It was the first major international conference on general relativity and gravitation held on the African continent.
General relativity (Physics) --- Gravitation --- Gravitational waves
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This volume offers a comprehensive overview of our understanding of gravity at both the experimental and the theoretical level. Critical reviews by experts cover topics ranging from astrophysics (anisotropies in the cosmic microwave background, gamma ray bursts, neutron stars and astroparticles), cosmology, the status of gravitational wave sources and detectors, verification of Newton's law at short distances, the equivalence principle, gravito-magnetism, measurement theory, time machines and the foundations of Einstein's theory, to string theory and loop quantum gravity.
General relativity (Physics) --- Particles (Nuclear physics)
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The thesis tackles two distinct problems of great interest in gravitational mechanics — one relativistic and one Newtonian. The relativistic one is concerned with the "first law of binary mechanics", a remarkably simple variational relation that plays a crucial role in the modern understanding of the gravitational two-body problem, thereby contributing to the effort to detect gravitational-wave signals from binary systems of black holes and neutron stars. The work reported in the thesis provides a mathematically elegant extension of previous results to compact objects that carry spin angular momentum and quadrupolar deformations, which more accurately represent astrophysical bodies than mere point particles. The Newtonian problem is concerned with the isochrone problem of celestial mechanics, namely the determination of the set of radial potentials whose bounded orbits have a radial period independent of the angular momentum. The thesis solves this problem completely in a geometrical way and explores its consequence on a variety of levels, in particular with a complete characterisation of isochrone orbits. The thesis is exceptional in the breadth of its scope and achievements. It is clearly and eloquently written, makes excellent use of images, provides careful explanations of the concepts and calculations, and it conveys the author’s personality in a way that is rare in scientific writing, while never sacrificing academic rigor.
Astrophysics --- Geophysics --- zwaartekracht --- astrofysica --- General relativity (Physics)
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This book investigates Lorentzian structures in the four-dimensional space-time, supplemented either by a covector field of the time-direction or by a scalar field of the global time. Furthermore, it proposes a new metrizable model of gravity. In contrast to the usual General Relativity theory, where all ten components of the symmetric pseudo-metric are independent variables, the gravity model presented here essentially depends only on a single four-covector field, and is restricted to have only three-independent components. However, the author proves that the gravitational field, governed by the proposed model and generated by some massive body, resting and spherically symmetric in some coordinate system, is given by a pseudo-metric that coincides with the well known Schwarzschild metric from General Relativity. The Maxwell equations and electrodynamics are also investigated in the framework of the proposed model. In particular, the covariant formulation of electrodynamics of moving dielectrics and para/diamagnetic media is derived.
Geophysics --- zwaartekracht --- General relativity (Physics) --- Quantum electrodynamics.
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Our vast Universe is filled with an enormous amount of matter and energy, which are the source of large gravitational potentials affecting all physical phenomena. Because this fact about the size and contents of the Universe was not known when our fundamental theories of dynamics and relativity were completed by the 1920s, the current theories - based as they are in empty space - fail to incorporate cosmic gravity. Though the current theories are consistent with the majority of empirical facts, there are some crucial discrepancies, which demand a drastic shift to a cosmic gravitational paradigm for the theories of relativity and dynamics. The book is a detailed and widely accessible account of this paradigm, called Cosmic Relativity, supported by ample empirical evidence. It is established that all motional relativistic effects are cosmic gravitational effects. The new theory of Cosmic Relativity solves and answers all outstanding questions and puzzles about dynamics and relativity.
Cosmology --- Geophysics --- zwaartekracht --- kosmologie --- General relativity (Physics)
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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 "dark matter" 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
General relativity (Physics) --- Gravity. --- Gravitational fields. --- Galaxies.
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This book is a compilation of the lectures for a one-semester course on gravitation at the University of Rochester. Starting from a simple description of geometry, the topics are systematically developed to the big bang theory with a simple derivation of the cosmic background temperature. Several informative examples are worked out in detail as well.
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