Charged Black Holes

Accurately ray-tracing a scene containing multiple black holes requires following light along null geodesics of a curved spacetime — in general, a computationally demanding problem involving nonlinear ODEs on a manifold known only numerically. This talk describes a beautiful exception: the Majumdar-Papapetrou exact solutions to the Einstein-Maxwell equations, describing multiple extremally charged black holes in static equilibrium, where gravitational attraction is precisely canceled by electrostatic repulsion. By exploiting conformal invariance of null geodesics, we reduce the relativistic raytracing problem to a classical one: tracing light through flat space with a spatially varying refractive index encoding the black hole configuration. Any renderer supporting variable indices of refraction can then produce exact images of these spacetimes — no relativistic simulator required.