黑洞时空中Terrell-Penrose效应的光线追踪
The Terrell-Penrose effect revisited and extended for black hole spacetime
AI总结：
本研究通过光线追踪模拟检验黑洞时空下的Terrell-Penrose效应，发现平直时空两种运动辐射源观测情况不等价，黑洞时空下情况i)共形变换仍成立、情况ii)引力产生额外影响。
摘要：
受M87星系和银河系黑洞近期图像的启发，高效相对论光线追踪技术被开发用于模拟黑洞周围可变辐射的快照。半个世纪前，Terrell和Penrose研究了运动辐射源的外观，他们独立发现像差效应会在观测者的天球上诱导共形变换，因此运动球体的快照应保持圆形。本研究通过光线追踪模拟检验Terrell-Penrose效应的两种对比情况：i) 运动观测者视角下的静态辐射源；ii) 静态观测者视角下的运动辐射源。在平直时空中，人们认为这两种情况下辐射源的图像因运动相对性而等价。我们的模拟表明，尽管两种情况的球体表观形状均保持不变，但图像的表观畸变不同，且情况ii)违反了观测者天球上的共形性。此外，我们将类似情况扩展到黑洞时空：对于情况i)，发现像差效应诱导的共形变换在黑洞时空中同样成立，且不限于测地运动的观测者；对于情况ii)，我们研究了运动源的慢光效应，结果表明引力对运动源的快照产生额外影响。
英文摘要：
Half a century ago, Terrell and Penrose independently studied the visual appearance of a moving sphere and found that the visual distortion can be formulated by a conformal transformation on the observer's celestial sphere. In this study, we examine the Terrell-Penrose effect by considering the images of spheres in two contrasting cases: i) a static sphere in the view of a moving observer, and ii) a moving sphere in the view of a static observer. In these two cases, the images are expected to be identical for flat spacetime because of the principle of relativity. However, utilizing ray-tracing simulations, our results find that the images are distinct, and in case ii) the image distortion violates conformality. We also extend the studies to Schwarzschild spacetime. In case i), we can obtain a natural extension, whereas in case ii), it is demonstrated that gravity introduces an additional influence on the images of moving objects.
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