史瓦西时空中的Pound-Rebka实验和挠率
Pound-Rebka experiment and torsion in the Schwarzschild spacetime
摘要：
我们发展了E. Schucking [arXiv：0803.4128]关于引力场的几何学。首先，我们提出这样一个概念，根据这个概念，引力加速度是时空挠率的表现，而不是曲率张量的表现。可以证明，在某些情况下，粒子的测地线加速度可以获得任意值，而曲率张量接近于零。我们的结论是时空曲率不影响测地线加速度。然后我们考虑Pound-Rebka实验，它将在位置$r_1$发射的两个光信号的时间间隔$Δτ_1$与在位置$r_2$接收的信号的时间间隔$Δτ_2$联系起来，在史瓦西型引力场中。实验由四个时空事件决定。由这些事件形成的无穷小矢量在（t，r）平面上不形成一个矢量。宇宙的闭合失败意味着时空有挠率。我们找到了扭转张量的显式形式，解释了非封闭的的。
英文摘要：
We develop some ideas discussed by E. Schucking [arXiv:0803.4128] concerning the geometry of the gravitational field. First, we address the concept according to which the gravitational acceleration is a manifestation of the spacetime torsion, not of the curvature tensor. It is possible to show that there are situations in which the geodesic acceleration of a particle may acquire arbitrary values, whereas the curvature tensor approaches zero. We conclude that the spacetime curvature does not affect the geodesic acceleration. Then we consider the the Pound-Rebka experiment, which relates the time interval $Δτ_1$ of two light signals emitted at a position $r_1$, to the time interval $Δτ_2$ of the signals received at a position $r_2$, in a Schwarzschild type gravitational field. The experiment is determined by four spacetime events. The infinitesimal vectors formed by these events do not form a parallelogram in the (t,r) plane. The failure in the closure of the parallelogram implies that the spacetime has torsion. We find the explicit form of the torsion tensor that explains the nonclosure of the parallelogram.
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