关于几何定义的相对速度计算的注记
A note on the computation of geometrically defined relative velocities
摘要：
讨论了广义相对论中几何定义的运动学、光谱学、费米和天体测量学相对速度的计算。我们主要指出，运动学和光谱学的相对速度只取决于观察者和测试粒子的4-速度，这与费米和天体测量学的相对速度不同，费米和天体测量学的相对速度也取决于观察者的加速度和测试粒子的相应相对位置，但只是在观察事件中，而不是在它周围，因为它原则上是从这些速度的定义中推导出来的。最后，我们提出了一个开放的问题，在广义相对论，包括寻找费米和天体测量相对速度的内在表达式，避免涉及测试粒子的相对位置的演变条款。为此，本文给出的证明可作为一种启示。
英文摘要：
We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike Fermi and astrometric relative velocities, that also depend on the acceleration of the observer and the corresponding relative position of the test particle, but only at the event of observation and not around it, as it would be deduced, in principle, from the definition of these velocities. Finally, we propose an open problem in general relativity that consists on finding intrinsic expressions for Fermi and astrometric relative velocities avoiding terms that involve the evolution of the relative position of the test particle. For this purpose, the proofs given in this paper can serve as inspiration.
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