觀察者運動方式對黑洞剪影大小所造成的影響

Abstract

黑洞與彎曲時空一直都是大眾喜愛的概念，如何將黑洞附近的彎曲時空 視覺化以及理解黑洞剪影特性皆是極具有科普價值的主題。在此論文中， 我們利用標架建立了在靜止黑洞附近史瓦西時空中運動的觀察者所接收到 光線的初始條件，計算測地線方程式並得到光線的軌跡，藉以探討黑洞剪 影的大小如何隨著觀察的位置與運動方式而改變。我們利用數值方法與半 解析解討論了黑洞剪影為何對在同樣位置但不同運動狀態的觀測者有不同 的張角，並示範了如何運用計算模擬算出觀察者在黑洞附近所看見的全天 影像。建立此全天圖的計算工具將可應用於虛擬實境的科普用途。

Black holes and curved space-time have always been popular con- cepts. How to visualize the curved space-time near black holes and understand the characteristics of black hole shadow is indeed a topic of great scientific value for popular science. In this paper, we use the tetrad to establish the initial condition of the light received by the observer moving in the Schwarzschild space-time near the static black hole, calculate the geodesic equation and then obtain the trajectory of the light, so as to inquire about the size of the black hole shadow changes with the location and motion of the observer. We use numerical methods and semi-analytical solution to discuss why the black hole shadow has different opening angles for observers at the same position but in different motion states, and demonstrate how to use computational simulations to calculate the full-sky image seen by observers near the black hole. Computational tools for building such an all-sky map will be applicable to popular science paths in virtual reality environments.