Visualization of the G\"odel universe

TL;DR

This paper uses ray tracing to visualize how an observer would perceive time travel in Kurt G"odel's rotating universe model, offering new insights into its space-time structure.

Contribution

It introduces a novel visualization approach applying computer graphics techniques to G"odel's universe, highlighting optical effects of time travel.

Findings

Visualizations of objects undergoing time travel in G"odel's universe.

Insights into the optical effects caused by the universe's rotation.

Enhanced understanding of G"odel's spacetime structure.

Abstract

The standard model of modern cosmology, which is based on the Friedmann-Lema\^itre-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 G\"odel, 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 G\"odel'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 G\"odel's model.