Expansions of the affinity, metric and geodesic equations in Fermi normal coordinates about a geodesic
Expansions of the affinity, metric and geodesic equations in Fermi normal coordinates about a geodesic
复制标题
费米法向坐标中关于测地线的亲和方程、度量方程和测地线方程的展开
DOI：
--
复制
发表时间：
1979
期刊：
影响因子：
--
通讯作者：
W. Ni
中科院分区：
文献类型：
--
作者：
Wann‐Quan Li;W. Ni
关于测地线的费米法向坐标形成了非旋转测地线（自由下落）观察者的自然坐标系。在这些坐标系中的亲和力，度量和测地线方程的扩展在这里计算到三阶，四阶和三阶，分别为适当的距离的权力，垂直于测地线。文中还给出了高阶计算的迭代格式。为了一般性，我们计算了任意仿射流形上的仿射方程和测地线方程，并计算了具有任意签名的黎曼流形上的度量。
Fermi normal coordinates about a geodesic form a natural coordinate system for the nonrotating geodesic (freely falling) observer. Expansions of the affinity, metric, and geodesic equations in these coordinates in powers of proper distance normal to the geodesic are calculated here to third order, fourth order, and third order, respectively. An iteration scheme for calculation to higher orders is also given. For generality, we compute the affinity and the geodesic equations in an arbitrary affine manifold, and compute the metric in a Riemannian manifold with arbitrary signature.