加速观测器的相对论像差
Relativistic Aberration for Accelerating Observers
摘要：
本文研究了匀加速观测者的光行差效应。我们考虑的观察者最初相对于一个发光的球形物体（比如说一颗恒星）静止，然后开始以恒定的加速度移动。我们得到的主要结果如下：（1）观察者总是看到一个初始增加的对象的表观大小;（2）的对象的表观大小接近一个非零值作为适当的时间的观察者走向无穷大。(iii)加速度存在一个临界值，使得当加速度超临界时，物体的视尺寸总是在增加。我们表明，虽然（i）是一个纯粹的非相对论效应，（ii）和（iii）是相对论性光行差的影响，并与闵可夫斯基时空的洛伦兹几何密切相关。最后，我们提供的例子表明，虽然这三种效应在日常生活中或多或少可以忽略不计，但在太空飞行的背景下可能很重要。
英文摘要：
We investigate the effects of the aberration of light for a uniformly accelerating observer. The observer we consider is initially at rest with respect to a luminous spherical object--a star, say--and then starts to move away with constant acceleration. The main results we derive are the following: (i) The observer always sees an initial increase of the apparent size of the object; (ii) The apparent size of the object approaches a non-zero value as the proper time of the observer goes to infinity. (iii) There exists a critical value of the acceleration such that the apparent size of the object is always increasing when the acceleration is super-critical. We show that, while (i) is a purely non-relativistic effect, (ii) and (iii) are effects of the relativistic aberration of light and are intimately connected with the Lorentzian geometry of Minkowksi spacetime. Finally, the examples we present illustrate that, while more or less negligible in everyday life, the three effects can be significant in the context of space-flight.
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