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Gravitation --- Modeles mathematiques --- Gravitation --- Modeles mathematiques

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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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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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Galaxies --- Millimeter waves --- Congresses --- Millimeter astronomy --- Cosmochemistry --- Astrophysics --- Molecular clouds --- Astrophysics. --- Observations, Astronomical. --- Astronomy—Observations. --- Gravitation. --- Astrophysics and Astroparticles. --- Astronomy, Observations and Techniques. --- Classical and Quantum Gravitation, Relativity Theory. --- Field theory (Physics) --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Astronomical observations --- Observations, Astronomical --- Astronomical physics --- Astronomy --- Cosmic physics --- Properties --- Millimeter-wave radio astronomy --- Millimetre astronomy --- Radio astronomy

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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