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Einstein's Special Relativity (E-SR) is the cornerstone of physics. De Sitter invariant SR (dS/AdS-SR) is a natural extension of E-SR, hence it relates to the foundation of physics. This book provides a description to dS/AdS-SR in terms of Lagrangian-Hamiltonian formulation associated with spacetime metric of inertial reference frames. One of the outstanding features of the book is as follows: All discussions on SR are in the inertial reference frames. This is a requirement due to the first principle of SR theory. The descriptions on dS/AdS-SR in this book satisfy this principle. For the curved spacetime in dS/AdS-SR theory, it is highly non-trivial. Contents:General IntroductionOverview of Einstein's Special Relativity (E-SR)De Sitter Invariant Special RelativityDe Sitter Invariant General RelativityDynamics of Expansion of the Universe in General RelativityRelativistic Quantum Mechanics for de Sitter Invariant Special RelativityDistant Hydrogen Atom in CosmologyTemporal and Spatial Variation of the Fine Structure ConstantDe Sitter Invariance of Generally Covariant Dirac Equation Readership: Students and professionals who are interested in de Sitter and anti-de Sitter invariant Special Relativity. Key Features:This is the first book to describe dS/AdS-SR systematically and comprehensivelyThe crucial contributions to dS/AdS-SR due to Lu–Zou–Guo's work (1970's) are interpreted in detail in this book. The conceptions of dS/AdS-SR Mechanics, dS/AdS-SR Quantum Mechanics, dS/AdS-SR General Relativity, and effects of dS/AdS-SR Cosmology are introduced in the book. In the descriptions, many techniques are involvedThe author, Professor Mu-Lin Yan, is an expert in SR, GR, Black Hole Physics, and Particle Physics. He is one of the discoverers of Nieh–Yan topological identity (1982), High genus solution of Yang–Baxter equation of chiral Potts model (1987), and some unusual hadron's states (2005). He also has contributions to the calculations of entropies of black holes, and to the studies of non-perturbative QCDKeywords:De Sitter Invariant Special Relativity;Special Relativity;De Sitter Group
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 34. Chapters: Acceleration, Rotation, Centripetal force, Universal joint, De Sitter invariant special relativity, Rotation operator, Instant centre of rotation, Velocity, Rational motion, Screw theory, Cell Transmission Model, Geneva drive, Klann linkage, Four-bar linkage, Burmester's theory, Kinematic pair, Mechanism, Kenneth H. Hunt, Heat current, Torricelli's equation, Screw joint, Revolute joint, Prismatic joint, Cylindrical joint, Center of mass coordinates, Centrode. Excerpt: Centripetal force (from Latin centrum "center" and petere "to seek") is a force that makes a body follow a curved path: it is always directed orthogonal to the velocity of the body, toward the instantaneous center of curvature of the path. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens. Isaac Newton's description was: "A centripetal force is that by which bodies are drawn or impelled, or in any way tend, towards a point as to a center." The magnitude of the centripetal force on an object of mass m moving at a speed v along a path with radius of curvature r is: where is the centripetal acceleration. The direction of the force is toward the center of the circle in which the object is moving, or the osculating circle, the circle that best fits the local path of the object, if the path is not circular. This force is also sometimes written in terms of the angular velocity ? of the object about the center of the circle: Expressed using the period for one revolution of the circle, T, the equation becomes: For a satellite in orbit around a planet, the centripetal force is supplied by gravity. Some sources, including Newton, refer to the entire force as a centripetal force, even for non-circular orbits, for which gravity is not aligned with the direction to the center of curvature. The gravitational force acts on each obj...
This book presents the Projective approach to de Sitter Relativity. It traces the development of renewed interest in models of the universe at constant positive curvature such as "vacuum" geometry. The De Sitter Theory of Relativity, formulated in 1917 with Willem De Sitter's solution of the Einstein equations, was used in different fields during the 1950s and 1960s, in the work of H. Bacry, J.M. LevyLeblond and F.Gursey, to name some important contributors. From the 1960s to 1980s, L. Fantappié and G. Arcidiacono provided an elegant group approach to the De Sitter universe putting the basis for special and general projective relativity. Today such suggestions flow into a unitary scenario, and this way the De Sitter Relativity is no more a "missing opportunity" (F. Dyson, 1972), but has a central role in theoretical physics. In this volume a systematic presentation is given of the De Sitter Projective relativity, with the recent developments in projective general relativity and quantum cosmology.
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 151. Chapters: Nash embedding theorem, Conformal map, Curvature, Geodesic, Riemannian manifold, Riemann curvature tensor, Metric tensor, Holonomy, Symmetric space, De Sitter invariant special relativity, Covariance and contravariance of vectors, Geometrization conjecture, Systolic geometry, Covariant derivative, Hodge dual, Einstein notation, Ricci curvature, Ricci flow, Spin structure, Exponential map, List of formulas in Riemannian geometry, Introduction to systolic geometry, Christoffel symbols, Laplace-Beltrami operator, Glossary of Riemannian and metric geometry, Parallel transport, Gauss-Codazzi equations, Curvature of Riemannian manifolds, Gauss's lemma, Uniformization theorem, Levi-Civita connection, Ricci decomposition, Second fundamental form, Sectional curvature, De Sitter-Schwarzschild metric, Poincar metric, Calibrated geometry, Gravitational instanton, De Sitter space, Calculus of moving surfaces, Hermitian manifold, Tortuosity, Weyl tensor, Scalar curvature, Harmonic map, Cartan-Hadamard theorem, Pseudo-Riemannian manifold, Lie bracket of vector fields, Hermitian symmetric space, Spherical 3-manifold, Geodesics as Hamiltonian flows, K hler manifold, Abel-Jacobi map, Jacobi field, Constraint counting, Clifford bundle, Killing vector field, Normal coordinates, Systoles of surfaces, Curved space, Fundamental theorem of Riemannian geometry, Theorema Egregium, Hyperk hler manifold, Unit tangent bundle, Sasakian manifold, Loewner's torus inequality, Cartan-Karlhede algorithm, Pu's inequality, Gauss map, Einstein manifold, Recurrent tensor, Soul theorem, Harmonic coordinates, Ruppeiner geometry, Filling radius, G2 manifold, Sub-Riemannian manifold, Quaternion-K hler manifold, Frobenius manifold, Gromov-Hausdorff convergence, Cheng's eigenvalue comparison theorem, Gromov's systolic inequality for essential manifolds, Macb...
These proceedings contain an up-to-date series of lectures covering issues at the forefront of cosmology, gravitation, and astrophysics. Both observational matters, such as accelerated expansion of the universe, and gamma ray bursts and theoretical issues, such as loop quantum gravity and quantum field theory in de Sitter space are presented. Being a school for advanced students, many of the lectures were a high level revision of recent developments, among which could single out the results presented by Belinski regarding the absence of black hole evaporation, and Riffini regarding the origin of gamma-0 ray bursts.
This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and other subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation. The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level of understanding, a more advanced treatment of the mathematical topics. It is aimed as an elementary text, more so than most others on the market, and is intended for first year graduate students. Contents:ManifoldsDifferentiable StructureFinal TouchMathematical TopicsPhysical TopicsGlossaryReferencesAlphabetic Index Readership: Mathematical physicists. keywords:Manifolds;Differential Geometry;Differential Forms;Symmetries;Variational Calculus;Hamiltonian Mechanics;Elasticity;Relativistic Fields;Gauge Fields;General Relativity
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 153. Chapters: Gravitational singularity, Wormhole, Cosmological constant, Cosmic censorship hypothesis, Weyl's postulate, Anti-gravity, BKL singularity, Alternatives to general relativity, Introduction to general relativity, Gravitational wave, Equivalence principle, History of general relativity, De Sitter invariant special relativity, Metric expansion of space, Maxwell's equations in curved spacetime, Theoretical motivation for general relativity, Mass in general relativity, Einstein field equations, Gravitomagnetism, Newtonian motivations for general relativity, Penrose-Hawking singularity theorems, Event horizon, Parameterized post-Newtonian formalism, Synchronous frame, Golden age of general relativity, Friedmann equations, Causal structure, Sticky bead argument, Introduction to mathematics of general relativity, Surface gravity, Geodesic, Light front holography, Raychaudhuri equation, Komar mass, Einstein-Hilbert action, Geometrized unit system, Hole argument, String cosmology, Gravitational shielding, Physical theories modified by general relativity, Linearized gravity, Geodetic effect, Cosmological perturbation theory, Gravitational field, Solutions of the Einstein field equations, Initial value formulation, CGHS model, Photon sphere, Causality conditions, Lense-Thirring precession, Solving the geodesic equations, General covariance, Weyl curvature hypothesis, Absolute horizon, Gravitational wave astronomy, Geon, Malament-Hogarth spacetime, Spacetime topology, Hawking energy, Globally hyperbolic manifold, Riemannian Penrose inequality, Gibbons-Hawking-York boundary term, Manifest covariance, Photon surface, Roman ring, ADM energy, Propagation of light in non-inertial reference frames, Abstract differential geometry, GRTensorII, Warped geometry, Retarded position, CLIO, Kugelblitz, Gravitomagnetic time delay, ..

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