静态球对称场的对角化坐标观点下的测地线方程和质能关系
Diagonal Metrics of Static, Spherically Symmetric Fields The Geodesic Equations and the Mass-Energy Relation from the Coordinate Perspective
摘要：
计算了静态球对称场对角度量一般情况下的测地线方程。通过消去固有时间变量，给出了试验粒子关于坐标时间的运动方程，并从坐标角度对引力加速度进行了解释。结果适用于史瓦西度量和所谓的指数度量。在尝试添加一个帐户的引力从坐标的角度来看，特殊的相对论性质能关系广义对角度量涉及的位置依赖性和可能各向异性的光速。这种移动需要区分测试粒子质量的两个方面（平行于场和垂直于场）。所得到的力的表达式不揭示引力排斥史瓦西度规和指数度规。
英文摘要：
The geodesic equations for the general case of diagonal metrics of static, spherically symmetric fields are calculated. The elimination of the proper time variable gives the motion equations for test particles with respect to coordinate time and an account of gravitational acceleration from the coordinate perspective. The results are applied to the Schwarzschild metric and to the so-called exponential metric. In an attempt to add an account of gravitational force from the coordinate perspective, the special relativistic mass-energy relation is generalized to diagonal metrics involving location dependent and possibly anisotropic light speeds. This move requires a distinction between two aspects of the mass of a test particle (parallel and perpendicular to the field). The obtained force expressions do not reveal gravitational repulsion for the Schwarzschild metric and for the exponential metric.
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