自由质点测地线仿射参量时空坐标系  

Free particle geodesic affine parameter time-space coordinate systems

作　　者：卞保民[1] 赖小明[1] 杨玲[1] 李振华[1] 贺安之[1] 

机构地区：[1]南京理工大学信息物理与工程系,南京210094

出　　处：《物理学报》2012年第17期33-45,共13页Acta Physica Sinica

摘　　要：以时序t为自变量,可给出自由质点空间测地线的参数方程组{X^i(t)},借助于仿射参量R(t)变换实现测地线微分方程的齐次化,推导出仿射参量R满足的一阶微分方程、获得以有理数C_u为标志的序列解析解R.基于R定义平直四维坐标系{t,r,θ,(?)}的空间距离单位,建立自由质点测地线仿射参量时空坐标系{t,ξ,θ,(?)}.研究{t,ξ,θ,(?)}中狭义相对论时空间隔模型度规张量g的对角化过程,发现与对角化度规对应的特征量t_1(t,ξ),τ_1(τ,ξ),t_t(t,τ,ξ),τ_(τ1)(t,τ,ξ);从而推出时空坐标系{t,ξ,θ,(?)}维数小于4.Taking the time-series t as independent variable, the parameter equations {Xi（t）} of free particle space geodesic can be given. By transforming affine parameter R（t） we achieve homogeneous geodesic differential equations, and derive the first-order differential equations which are satisfied by affine parameter R and the sequence of analytical solutions R marked by rational number Cu. In light of R we define the distance unit of flat four-dimensional coordinate system {t,r,θ,φ}, and then establish a free particle geodesic affine parameter time-space coordinate system {t,ξ,θ,φ}. By the study of the diagonalization process of special relativity time-space interval model metric tensor g in {t,ξ,θ,φ}, we find the spatial and temporal line characteristic quantities t1（t,ξ）, τ1（τ,ξ）,tt（t,τ,ξ） and ττ1（t,τ,ξ） corresponding to diagonal metric. Derived from these quantities, the dimension of time-space coordinate system is less than 4.

关 键 词：广义相对论 测地线仿射参量 时空度规 

分 类 号：O412.1[理学—理论物理]