英和和英

出典:『Wikipedia』 (2011/04/12 03:53 UTC 版)

英語による解説

引用

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.