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dc.contributor.authorGourgoulhon, Ericen_US
dc.date.accessioned2017-06-16T04:03:00Z
dc.date.available2017-06-16T04:03:00Z
dc.date.issued2012en_US
dc.identifier.isbn978-3-642-24524-4en_US
dc.identifier.otherHPU5160054en_US
dc.identifier.urihttps://lib.hpu.edu.vn/handle/123456789/25408
dc.description.abstractThis 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.en_US
dc.format.extent303 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.subjectRelativityen_US
dc.subject3+1 Formalismen_US
dc.subjectNumerical Relativityen_US
dc.title3+1 Formalism in General Relativity: Bases of Numerical Relativityen_US
dc.typeBooken_US
dc.size2,015Kben_US
dc.departmentTechnologyen_US


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