01 / LIGHT IN ROTATING SPACETIME
Kerr Black Hole
Two incoming rays. One spinning spacetime. Different outcomes.
GEODESIC EXPERIMENT
Follow the light, measure the bending
Equatorial Boyer–Lindquist coordinate map · not a camera image
PREDICTION
Capture thresholds change with spin
Equations, assumptions & model scope +
Geodesics, not an optical photograph
G = M = c = 1. Two equatorial null geodesics have E = 1 and b = Lz/E. The radial potential is R = (r² + a² − ab)² − Δ(b − a)², with Δ = r² − 2r + a². Adaptive RK4 step doubling controls scaled local error at 10⁻¹⁰, and the null radial constraint is checked independently.
Incoming rays start at r = 24M, with their direction set by quadrature from infinity. Outgoing rays receive an angular tail correction to infinity. The reported unwrapped bending includes winding; the number is available only after scattering. Playback uses affine parameter, not time seen by a distant observer.
Capture is stopped just outside the horizon, at r₊ + 0.001M. A duration cutoff is not proof of permanent orbiting. Colored photon-orbit circles are unstable equatorial geodesics, not an observed photon ring. The amber region is between the equatorial horizon and the stationary limit r = 2M.
This experiment does not implement inclined trajectories, a ray-traced camera, an accretion disk, or horizon-interior evolution.
Background: Tong · black-hole geometry · REBOUND · a reference for high-accuracy gravitational integration. This experiment uses its own RK4-based solver, not IAS15.