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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク CGHS model ： ウィキペディア英語版 CGHS model The Callan–Giddings–Harvey–Strominger model or CGHS〔 〕 in short is a toy model of general relativity in 1 spatial and 1 time dimension. General relativity is a highly nonlinear model, and as such, its 3+1D version is usually too complicated to analyze in detail. In 3+1D and higher, propagating gravitational waves exist, but not in 2+1D or 1+1D. In 2+1D, general relativity becomes a topological field theory with no local degrees of freedom, and all 1+1D models are locally flat. However, a slightly more complicated generalization of general relativity which includes dilatons will turn the 2+1D model into one admitting mixed propagating dilaton-gravity waves, as well as making the 1+1D model geometrically nontrivial locally.〔 〕〔 〕 The 1+1D model still does not admit any propagating gravitational (or dilaton) degrees of freedom, but with the addition of matter fields, it becomes a simplified, but still nontrivial model. With other numbers of dimensions, a dilaton-gravity coupling can always be rescaled away by a conformal rescaling of the metric, converting the Jordan frame to the Einstein frame. But not in two dimensions, because the conformal weight of the dilaton is now 0. The metric in this case is more amenable to analytical solutions than the general 3+1D case. And of course, 0+1D models cannot capture any nontrivial aspect of relativity because there is no space at all. This class of models retains just enough complexity to include among its solutions black holes, their formation, FRW cosmological models, gravitational singularities, etc. In the quantized version of such models with matter fields, Hawking radiation also shows up, just as in higher-dimensional models. == Action == A very specific choice of couplings and interactions leads to the CGHS model. :$S\; =\; \backslash frac\; \backslash int\; d^2x\backslash ,\; \backslash sqrt\backslash left\backslash \; \backslash frac\backslash left(\; \backslash nabla\; f\_i\; \backslash right)^2\; \backslash right\backslash \}$ where ''g'' is the metric tensor, ''φ'' is the dilaton field, ''fi'' are the matter fields, and ''λ2'' is the cosmological constant. In particular, the cosmological constant is nonzero, and the matter fields are massless real scalars. This specific choice is classically integrable, but still not amenable to an exact quantum solution. It is also the action for Non-critical string theory and dimensional reduction of higher-dimensional model. It also distinguishes it from Jackiw–Teitelboim gravity and Liouville gravity, which are entirely different models. The matter field only couples to the causal structure, and in the light-cone gauge , has the simple generic form :$f\_i\backslash left(\; u,\; v\; \backslash right)\; =\; A\_i\backslash left(\; u\; \backslash right)\; +\; B\_i\; \backslash left(\; v\; \backslash right)$, with a factorization between left- and right-movers. The Raychaudhuri equations are :$e^\; \backslash left(\; -\; 2\backslash phi\_\; +\; 4\; \backslash rho\_\backslash phi\_\; \backslash right)\; +\; f\_f\_/2=\; 0$ and :$e^\; \backslash left(\; -\; 2\backslash phi\_\; +\; 4\; \backslash rho\_\backslash phi\_\; \backslash right)\; +\; f\_f\_/2=\; 0$. The dilaton evolves according to :$\backslash left(\; e^\; \backslash right)\_\; =\; -\; \backslash lambda^2\; e^e^$, while the metric evolves according to :$2\backslash rho\_\; -\; 4\backslash phi\_\; +\; 4\backslash phi\_\backslash phi\_\; +\; \backslash lambda^2\; e^\; =\; 0$. The conformal anomaly due to matter induces a Liouville term in the effective action. 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「CGHS model」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.