Wind turbine WTG‑04 The left machine runs. The right model learns from it, predicts what it will do next, and says what to do about it.

The Observer slider sets the orbit radius r used by the two rows above — nothing is drawn for it, so the traced image stays exactly what the equations produce.

The numbers are exact. Every value above is computed live from the Schwarzschild solution, in SI units, from the mass you set — no lookup tables.

The image is traced, not drawn. For every pixel a light ray is followed backwards through Schwarzschild spacetime by integrating the photon orbit equation d²u/dφ² = −u + 1.5 r_su² with a Runge–Kutta solver. The arcs over the top and under the bottom are the second and third times that ray crosses the disk plane — nobody drew them. The shadow is simply where rays end on the horizon, which is why it comes out at 2.6 r_s by itself. The solver was checked against the exact capture impact parameter 3√3/2 r_s and reproduces it to better than 0.1%, so the shadow keeps its correct size even when the quality drops on a slower machine. Switch Lensing off to integrate straight lines instead and watch the arcs vanish.

What spin does here. The Spin slider uses exact Kerr formulas for the horizon, the photon sphere, the innermost stable orbit and the orbital frequency, so the disk really does close in, speed up and rise in pitch as you spin the hole up. But the ray tracing is still the Schwarzschild equation, so the image does not yet show the sideways squash that frame dragging gives a real Kerr shadow. Past about a = 0.35 the drawn inner edge of the disk stops moving, because the Kerr ISCO would fall inside the Schwarzschild shadow and vanish — an artefact of mixing two geometries, not physics. Treat every number as exact, and the shadow shape as the non‑rotating case.

What is still approximate. The disk's radial brightness now follows the standard Shakura–Sunyaev thin‑disk profile rather than an invented gradient, but it is still not a radiative‑transfer solution: the fine filaments are synthetic noise standing in for turbulence, and the colour is illustrative — at roughly 10⁷ K a real disk emits X‑rays your eye could not see. The step budget truncates rays that loop many times, so the very highest‑order images are missing. Sizes are not to scale: a real star is around 10⁵ r_s across, so it cannot be drawn beside its own horizon, and the collapse takes seconds here and milliseconds in reality.

The shape arises for the same reason the film's did: the disk is viewed almost edge‑on, and light from the far side is bent up over the hole and down under it, closing into a ring around the shadow. Both images come out of the same integration.

About the sound. A vacuum carries no sound, so none of this is what you would hear. It is sonification: the pitch is the orbital frequency at the innermost stable orbit, which really is 220 Hz for a 10 M_☉ hole and rises to 1361 Hz at the Thorne spin limit. It is placed at the hole with HRTF panning and fed through convolution reverb, and the listener follows your camera, so orbiting moves the sound around your head. The supernova is a synthesised burst, not a measurement.

Gargantua left out Doppler beaming on purpose. Kip Thorne's equations gave one side blindingly bright and the other nearly black; the filmmakers removed it because audiences found the lopsided image confusing. Switch Beaming off to match the film, and on to see what the physics actually predicts — an 81:1 brightness ratio.