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{Xi（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Cu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,φ}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,φ}.研究{t,ξ,θ,φ}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t1（t,ξ）, τ1（τ,ξ）,tt（t,τ,ξ）,ττ1（t,τ,ξ）; 从而推出时空坐标系{t,ξ,θ,φ}维数小于4.
Abstract:
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.
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