Lightfall

The Mathematics

The light cones here are surfaces swept out in spacetime by all the light rays leaving an event — not an infinitesimal cone in the tangent space, but the real, extended history of a spreading flash. Curvature (such as near a black hole) dramatically reshapes them, but for almost any multi–black-hole system they are prohibitively hard to compute, since the holes inspiral and shed energy as gravitational radiation. One remarkable exception is a static multi–black-hole solution where the mathematics stays just tractable enough: these images show the light cones of such Majumdar–Papapetrou spacetimes.

Technique

I wrote a general-relativistic geodesic integrator and computed the light cones for rays spreading out within a plane. These rays stay in a 2+1‑dimensional slice of the spacetime, so their light cones do too. Tracing thousands of geodesics, I built a mesh for each cone and rendered the result with a custom path tracer.