翻訳と辞書 Words near each other ・ Gaussian process ・ Gaussian process emulator ・ Gaussian q-distribution ・ Gaussian quadrature ・ Gaussian quantum Monte Carlo ・ Gaussian random field ・ Gaussian rational ・ Gaussian surface ・ Gaussian units ・ Gaussian year ・ Gaussig House ・ Gaussiran Glacier ・ Gausson ・ Gausson (physics) ・ Gauss–Boaga projection ・ Gauss–Bonnet gravity ・ Gauss–Bonnet theorem ・ Gauss–Codazzi equations ・ Gauss–Hermite quadrature ・ Gauss–Jacobi quadrature ・ Gauss–Kronrod quadrature formula ・ Gauss–Krüger coordinate system ・ Gauss–Kuzmin distribution ・ Gauss–Kuzmin–Wirsing operator ・ Gauss–Laguerre quadrature ・ Gauss–Legendre algorithm ・ Gauss–Legendre method ・ Gauss–Lucas theorem ・ Gauss–Manin connection ・ Gauss–Markov Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gauss–Bonnet gravity ： ウィキペディア英語版 Gauss–Bonnet gravity In general relativity, Gauss–Bonnet gravity, also referred to as Einstein–Gauss–Bonnet gravity, is a modification of the Einstein–Hilbert action to include the Gauss–Bonnet term (named after Carl Friedrich Gauss and Pierre Ossian Bonnet) $G=\; R^2\; -\; 4R^R\_\; +\; R^R\_$ :$\backslash int\; d^Dx\; \backslash sqrt\backslash ,\; G$ This term is only nontrivial in 4+1D or greater, and as such, only applies to extra dimensional models. In 3+1D and lower, it reduces to a topological surface term. This follows from the generalized Gauss–Bonnet theorem on a 4D manifold :$\backslash frac\backslash int\; d^4x\; \backslash sqrt\backslash ,\; G\; =\; \backslash chi(M)$. Despite being quadratic in the Riemann tensor (and Ricci tensor), terms containing more than 2 partial derivatives of the metric cancel out, making the Euler–Lagrange equations second order quasilinear partial differential equations in the metric. Consequently, there are no additional dynamical degrees of freedom, as in say f(R) gravity. More generally, we may consider :$\backslash int\; d^Dx\; \backslash sqrt\backslash ,\; f\backslash left(\; G\; \backslash right)$ term for some function ''f''. Nonlinearities in ''f'' render this coupling nontrivial even in 3+1D. However, fourth order terms reappear with the nonlinearities. == See also == * Einstein–Hilbert action * f(R) gravity * Lovelock gravity 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gauss–Bonnet gravity」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.