标题： 一个广义相对论摆：等时运动与测地线运动 显示英文标题

标题： A General Relativistic Pendulum: Isochronous vs. Geodesic Motion

摘要： 广义相对论（GR）被证明在钟摆的等时性方面是一个完整的理论。 这保证了在理论本身中，时间原则上可以通过机械钟进行测量。 简单钟摆的固有频率和坐标频率作为三个坐标参数的函数进行计算：支点到重力源的距离、其长度和施瓦茨希尔德半径。 在施瓦茨希尔德坐标中出现新的GR效应，表现为振荡频率的发散、零点和其他不稳定性，这些在牛顿引力中是不存在的。 在极端条件下会出现固有频率和坐标频率的异常：要么支点，要么钟摆质量，或者两者都位于事件视界之内。 显示英文摘要

摘要： General Relativity (GR) is shown to be a complete theory with respect to the isochrony of the pendulum. This guarantees that time can be measured with a mechanical clock within the theory itself as a matter of principle. The proper and coordinate oscillation frequencies of a simple pendulum are computed as a function of 3 coordinate parameters: the distance of the fulcrum to the gravity source, its length and the Schwarzschild radius. Novel GR effects appear in the Schwarzschild coordinates as divergences, zeroes and other instabilities of the oscillation frequencies that are absent in Newtonian gravity. The anomalies in the proper and coordinate frequencies occur under extreme conditions: either the fulcrum or the pendulum mass or both remain inside the Event Horizon.