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General relativity is a cornerstone of modern physics, and is of major importance in its applications to cosmology. Plebanski and Krasinski are experts in the field and in this 2006 book they provide a thorough introduction to general relativity, guiding the reader through complete derivations of the most important results. Providing coverage from a unique viewpoint, geometrical, physical and astrophysical properties of inhomogeneous cosmological models are all systematically and clearly presented, allowing the reader to follow and verify all derivations. For advanced undergraduates and graduates in physics and astronomy, this textbook will enable students to develop expertise in the mathematical techniques necessary to study general relativity.

General relativity (Physics) --- Quantum cosmology --- Quantum cosmology. --- General relativity (Physics). --- Cosmology --- Quantum theory --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics --- Relativity (Physics)

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Algemene relativiteitstheorie --- General relativity (Physics) --- Relativiteit [Algemene ] (Fysica) --- Relativiteitstheorie [Algemene ] --- Relativité générale (Physique) --- #dd Sabbe Camiel cfx --- 530.12 --- 530.12 Relativity principle --- Relativity principle --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics --- Relativity (Physics)

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Thoroughly revised and updated, this textbook provides a pedagogical introduction to relativity. It is self-contained, but the reader is expected to have a basic knowledge of theoretical mechanics and electrodynamics. It covers the most important features of both special and general relativity, as well as touching on more difficult topics, such as the field of charged pole-dipole particles, the Petrov classification, groups of motions, gravitational lenses, exact solutions and the structure of infinity. The necessary mathematical tools (tensor calculus, Riemannian geometry) are provided, most of the derivations are given in full, and exercises are included where appropriate. Written as a textbook for undergraduate and introductory graduate courses, it will also be of use to researchers working in the field. The bibliography gives the original papers and directs the reader to useful monographs and review papers.

Gravitational fields --- General relativity (Physics) --- Champs gravitationnels --- Relativité générale (Physique) --- Gravitational fields. --- Relativité générale (Physique) --- 530.12 --- 530.12 Relativity principle --- Relativity principle --- Fields, Gravitational --- Field theory (Physics) --- Gravitation --- Gravity --- Relativistic theory of gravitation --- Relativity theory, General --- Physics --- Relativity (Physics) --- Theory of relativity. Unified field theory --- General relativity (Physics).

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Algemene relativiteitstheorie --- Astrometrie --- Astrometry --- Astrométrie --- Celestial mechanics --- General relativity (Physics) --- Gravitational astronomy --- Hemelmechanica --- Mechanica [Hemel] --- Mechanics [Celestial ] --- Mécanique céleste --- Relativiteit [Algemene ] (Fysica) --- Relativiteitstheorie [Algemene ] --- Relativité générale (Physique) --- 521.1 --- Mechanics, Celestial --- Astrophysics --- Mechanics --- Positional astronomy --- Spherical astronomy --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics --- Relativity (Physics) --- Celestial mechanics. General principles of dynamical astronomy --- Astrometry. --- Celestial mechanics. --- General relativity (Physics). --- 521.1 Celestial mechanics. General principles of dynamical astronomy --- Mechanics, Celestial.

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This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.

General relativity (Physics) --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Physics - General --- Physics. --- Mathematics. --- Natural philosophy --- Philosophy, Natural --- Relativistic theory of gravitation --- Relativity theory, General --- Computer mathematics. --- Gravitation. --- Astronomy. --- Astrophysics. --- Cosmology. --- Numerical and Computational Physics. --- Classical and Quantum Gravitation, Relativity Theory. --- Astronomy, Astrophysics and Cosmology. --- Computational Mathematics and Numerical Analysis. --- Physical sciences --- Dynamics --- Gravitation --- Relativity (Physics) --- Computer science --- Numerical and Computational Physics, Simulation. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Astronomical physics --- Astronomy --- Cosmic physics --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Properties