Mechanics and Newton-Cartan-like gravity on the Newton-Hooke space-time
Mechanics and Newton-Cartan-like gravity on the Newton-Hooke space-time
复制标题
DOI：
10.1103/physrevd.71.044030
复制
发表时间：
2004-10
影响因子：
5
通讯作者：
Yu Tian;Han-Ying Guo;Chao-guang Huang;Zhan Xu;Bin Zhou
中科院分区：
文献类型：
--
作者：
Yu Tian;Han-Ying Guo;Chao-guang Huang;Zhan Xu;Bin Zhou
我们主要从de Sitter时空在Beltrami度规下的几何收缩的观点出发，研究了Newton-Hooke时空NH+的动力学性质。(The术语时空用于表示具有非退化度量的空间，而术语时空用于表示具有退化度量的空间。我们首先在这个框架下讨论了牛顿-胡克经典力学，特别是连续介质力学。然后，我们在Newton-Hooke时空上建立了一个相容的引力理论，它是一种类似Newton-Cartan的理论，与Galilei时空中的牛顿引力理论相平行。最后，我们从几何收缩出发，给出了Newton-Hooke不变量Schrodinger方程，在此方程中，我们可以将Newton-Hooke连续介质力学中的守恒几率在某种意义上与质量密度联系起来。类似的考虑可能适用于从反德西特时空收缩的牛顿-胡克时空NH-。
We focus on the dynamical aspects on Newton-Hooke space-time NH+ mainly from the viewpoint of geometric contraction of the de Sitter spacetime with Beltrami metric. (The term spacetime is used to denote a space with non-degenerate metric, while the term space-time is used to denote a space with degenerate metric.) We first discuss the Newton-Hooke classical mechanics, especially the continuous medium mechanics, in this framework. Then, we establish a consistent theory of gravity on the Newton-Hooke space-time as a kind of Newton-Cartan-like theory, parallel to the Newton's gravity in the Galilei space-time. Finally, we give the Newton-Hooke invariant Schrodinger equation from the geometric contraction, where we can relate the conservative probability in some sense to the mass density in the Newton-Hooke continuous medium mechanics. Similar consideration may apply to the Newton-Hooke space-time NH- contracted from anti-de Sitter spacetime.