Visualization of Analytical and Numerical Spacetimes Using Raytracing in Unity 3D

We present a ray marching code to visualize analytical and numerical spacetimes based on Unity 3D. Unity 3D is a free, cross-platform video game engine. Ray marching is an incremental version of ray tracing, an increasingly common graphics rendering technique in which the physics of the light rays that enter the camera are calculated based on the geometry of the scene. The paths of the light rays are found by integrating the geodesic equations numerically using an adaptive step-sizing RK2 technique. We bypass the use of the Christoffel symbols by calculating the derivatives of the spacetime metric, using a finite-differencing method. We have the option of using analytic spacetimes, such as the standard Schwarzschild metric, or using numeric spacetimes. We visualize the region beyond the event horizon by considering a numerical, puncture spacetime generated using the Z4c formalism of numerical relativity and interpolating as needed.