哥德尔宇宙的可视化
Visualization of the Gödel universe
摘要：
现代宇宙学的标准模型是以弗里德曼-勒梅特-罗伯逊-沃克度规为基础的，它允许绝对时间的定义。然而，存在与广义相对论一致的（宇宙学）模型，因为它们提供了时间旅行的可能性，所以不能给出这样的定义。这些模型中最简单的是库尔特·哥德尔发现的宇宙学解，它描述了一个均匀的、旋转的宇宙。撇开在这样的时空中因果关系的废除所带来的悖论不谈，我们感兴趣的是一个纯粹的学术问题，即观察者如何在视觉上感知哥德尔宇宙中物体的时间旅行。为此，我们采用光线跟踪技术，计算机图形学中的标准工具，并可视化各种场景，以显示位于这个宇宙中的观察者所经历的光学效果。通过这种方式，我们为哥德尔模型的时空结构提供了一个新的视角。
英文摘要：
The standard model of modern cosmology, which is based on the Friedmann-Lemaître-Robertson-Walker metric, allows the definition of an absolute time. However, there exist (cosmological) models consistent with the theory of general relativity for which such a definition cannot be given since they offer the possibility of time travel. The simplest of these models is the cosmological solution discovered by Kurt Gödel, which describes a homogeneous, rotating universe. Disregarding the paradoxes that come along with the abolishment of causality in such spacetimes, we are interested in the purely academical question how an observer would visually perceive the time travel of an object in Gödel's universe. For this purpose, we employ the technique of ray tracing, a standard tool in computer graphics, and visualize various scenarios to bring out the optical effects experienced by an observer located in this universe. In this way, we provide a new perspective on the space-time structure of Gödel's model.
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