| 期刊全稱 | 3+1 Formalism in General Relativity | | 期刊簡(jiǎn)稱 | Bases of Numerical R | | 影響因子2023 | Eric Gourgoulhon | | 視頻video | http://file.papertrans.cn/101/100629/100629.mp4 | | 發(fā)行地址 | Introductory text based on lectures and graduate-level courses.Detailed derivations make this a self-contained and complete exposition of the subject matter.Authored by a leading experts in the field. | | 學(xué)科分類 | Lecture Notes in Physics | | 圖書封面 |  | | 影響因子 | .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 ma | | Pindex | Book 2012 |
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