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This is an introductory textbook on applications of general relativity to astrophysics and cosmology. The aim is to provide graduate students with a toolkit for understanding astronomical phenomena that involve velocities close to that of light or intense gravitational fields. The approach taken is first to give the reader a thorough grounding in special relativity, with space-time the central concept, following which general relativity presents few conceptual difficulties. Examples of relativistic gravitation in action are drawn from the astrophysical domain. The book can be read on two levels: first as an introductory fast-track course, and then as a detailed course reinforced by problems which illuminate technical examples. The book has extensive links to the literature of relativistic astrophysics and cosmology.
General relativity (Physics) --- Astrophysics. --- Cosmology.
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Neutron stars --- Pulsars --- Relativity (Physics) --- Congresses --- Internal structure --- General relativity (Physics)
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Cosmology --- Gravitation. --- General relativity (Physics) --- Relativistic theory of gravitation --- Relativity theory, General --- Field theory (Physics) --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Gravitation --- Properties
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Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear, concise and up-to-date introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. All physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas are illustrated with worked examples. Solutions and hints to selected problems are provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity.
General relativity (Physics). --- Geometrodynamics. --- Space and time. --- Theory of relativity. Unified field theory --- General relativity (Physics) --- Space and time --- Geometrodynamics --- Relativité générale (Physique) --- Espace et temps --- 530.12 --- 530.12 Relativity principle --- Relativity principle --- 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) --- Geometry --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics
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This textbook is for mathematicians and mathematical physicists and is mainly concerned with the physical justification of both the mathematical framework and the foundations of the theory of general relativity. Previous knowledge of the relevant physics is not assumed. This book is also suitable as an introduction to pseudo-Riemannian geometry with emphasis on geometrical concepts. A significant part of the text is devoted to the discussion of causality and singularity theorems. The insights obtained are applied to black hole astrophysics, thereby making the connection to current active research in mathematical physics and cosmology.
Geometry, Differential --- Space and time --- General relativity (Physics) --- General relativity (Physics). --- Geometry, Differential. --- Space and time. --- Theory of relativity. Unified field theory --- Differential geometry. Global analysis --- Astrophysics. --- Gravitation. --- Astronomy. --- Physics. --- Differential geometry. --- Astrophysics and Astroparticles. --- Classical and Quantum Gravitation, Relativity Theory. --- Astronomy, Astrophysics and Cosmology. --- Mathematical Methods in Physics. --- Differential Geometry. --- Differential geometry --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Field theory (Physics) --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Astronomical physics --- Astronomy --- Cosmic physics --- Properties --- Data processing. --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- 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
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Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear, concise and up-to-date introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. All physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas are illustrated with worked examples. Solutions and hints to selected problems are provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity.
General relativity (Physics) --- Space and time. --- Geometrodynamics. --- Geometry --- Relativity (Physics) --- 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 --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics
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General relativity (Physics) --- Quantum theory --- Cosmology --- Space and time --- Astrophysics --- Relativité générale (Physique) --- Théorie quantique --- Cosmologie --- Espace et temps --- Astrophysique --- Congresses --- Congresses --- Congresses --- Congresses --- Congresses --- Congrès --- Congrès --- Congrès --- Congrès --- Congrès --- Schucking, E. L.
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