论文标题
牛顿重力近似的费米正常坐标
Fermi-normal coordinates for the Newtonian approximation of gravity
论文作者
论文摘要
在这项工作中，我们计算了对应于一般相对论弱场中静态和球体对称质量分布的度量标准，以围绕径向地球的费米正常坐标中的二次序列。为了构建沿其运输的大地测量和方便的四色，我们首先引入一个通用度量标准，使用差异形式的cartan形式，然后通过考虑几乎牛顿度量的时间来专业。该过程大大简化了计算，径向测量的表达式允许一种简单的形式。我们得出的结论是，按二次阶，通过自由下落的观察者在本地测量的施瓦茨柴尔兹柴尔德引力场的影响等于在牛顿的引力近似存在下，观察者在相似条件下通过观察者进行了测量。
In this work, we compute the metric corresponding to a static and spherically symmetric mass distribution in the general relativistic weak field approximation to quadratic order in Fermi-normal coordinates surrounding a radial geodesic. To construct a geodesic and a convenient tetrad transported along it, we first introduce a general metric, use the Cartan formalism of differential forms, and then specialize the space-time by considering the nearly Newtonian metric. This procedure simplifies the calculations significantly, and the expression for the radial geodesic admits a simple form. We conclude that in quadratic order, the effects of a Schwarzschild gravitational field measured locally by a freely falling observer equals the measured by an observer in similar conditions in the presence of a Newtonian approximation of gravitation.
