Non-linear Monte Carlo Ray Tracing for Visualizing Warped Spacetime

Abstract

General relativity describes the curvature of spacetime. Rays of light follow geodesic paths in curved spacetime. Visualizing scenes containing spacetime regions with pronounced curvature requires tracing of these light ray paths. We present a Monte Carlo approach for non-linear raytracing to render scenes in curved spacetime. In contrast to earlier work, we can accurately resolve ray-object interactions. This allows us to create plausible visualizations of what happens when a black hole appears in a more known environment, like a room with regular specular and diffuse surfaces. We demonstrate that our solution is correct at cosmological scales by showing how spacetime warps around a stationary Schwarzschild black hole and a non-stationary Kerr black hole. We verify that the solution is consistent with the predictions of general relativity. In the absence of any curvature in spacetime, our renderer behaves like a normal linear ray tracer. Our method has the potential to create rich, physically plausible visualizations of complex phenomena that can be used for a range of purposes, from creating visual effects to making pedagogical aids to understand the behaviour of spacetime as predicted by general relativity.