The Godel Engine - An interactive approach to visualization in general relativity

We present a methodical new approach to visualize the aspects of general relativity front a self-centered perspective. We focus on the visualization of the Godel universe, which is an exact solution to Einstein's field equations of general relativity. This model provides astounding features such as the existence of an optical horizon and the possibility of time travel. Although we know that our universe is not of Godel type, we can - using this solution to Einstein's equations - visualize and understand the effects resulting from the theory of relativity, which itself has been verified on the large scale in numerous experiments over the last century We derive the analytical solution to the geodesic equations of Godel's universe for special initial conditions. Along with programmable graphics hardware we achieve a tremendous speedup for the visualization of general relativity. This enables us to interactively explore the physical aspects and optical effects of Godel's universe. We also demonstrate how the analytical solution enables dynamic lighting with local illumination models. Our implementation is tailored for Godel's universe and five orders of magnitude faster than previous approaches. It can be adapted to manifolds for which an analytical expression of the propagation of light is available.