Visiting the Gödel Universe

Visualization of general relativity illustrates aspects of Einstein's insights into the curved nature of space and time to the expert as well as the layperson. One of the most interesting models which came up with Einstein's theory was developed by Kurt Gödel in 1949. The Gödel universe is a valid solution of Einstein's field equations, making it a possible physical description of our universe. It offers remarkable features like the existence of an optical horizon beyond which time travel is possible. Although we know that our universe is not a Gödel universe, it is interesting to visualize physical aspects of a world model resulting from a theory which is highly confirmed in scientific history. Standard techniques to adopt an egocentric point of view in a relativistic world model have shortcomings with respect to the time needed to render an image as well as difficulties in applying a direct illumination model. In this paper we want to face both issues to reduce the gap between common visualization standards and relativistic visualization. We will introduce two techniques to speed up recalculation of images by means of preprocessing and lookup tables and to increase image quality through a special optimization applicable to the Gödel universe. The first technique allows the physicist to understand the different effects of general relativity faster and better by generating images from existing datasets interactively. By using the intrinsic symmetries of Gödel's spacetime which are expressed by the Killing vector field, we are able to reduce the necessary calculations to simple cases using the second technique. This even makes it feasible to account for a direct illumination model during the rendering process. Although the presented methods are applied to Gödel's universe, they can also be extended to other manifolds, for example light propagation in moving dielectric media. Therefore, other areas of research can benefit from these generic improvements.