Blue Hole

How Blue Hole works

For every pixel, your graphics card follows one ray of light backward from the camera through the spacetime of a rotating black hole, the Kerr solution of Einstein's equations. It uses Carter's constants of motion and takes a few hundred Runge–Kutta steps per ray. A ray ends when it hits the disk, falls through the horizon, or escapes to the sky. At full resolution that is hundreds of millions of steps per frame.

What is computed

• Lensing: exact light paths in the Kerr metric (Boyer–Lindquist coordinates, Mino time), including the shadow, the photon ring and the higher-order images.
• Colour: the disk glows as a blackbody at each radius, with a thin-disk temperature profile that falls to zero at the ISCO. Light arrives shifted by g = ν_seen/ν_emitted, which combines the Doppler shift, gravitational redshift and your own motion. A blackbody at T seen through a shift g is exactly a blackbody at g·T, so colour and brightness (beaming) come from one table. That table is built from the CIE 1931 colour-matching functions, as elsewhere on this site.
• Stars are shifted the same way. Lensing conserves surface brightness, so magnified stars brighten near the Einstein ring. Emission nebulae shift as spectral lines.
• Your camera can hover, orbit or fall freely. Its motion adds aberration and Doppler shifts, and near the hole the outside world blueshifts.
• The probe and the fall follow timelike geodesics in the same spacetime. The probe's pings are spaced by its own proper time and pitched by its redshift.

What is simplified

• The disk is geometrically thin and opaque, with turbulence drawn from noise. Real disks are thicker and messier. The light-travel time to the probe is ignored.
• The "Radio" look blurs a synchrotron-like glow to the Event Horizon Telescope's 20 µas resolution. It is not a plasma simulation.
• "True heat" uses a standard thin disk accreting at 10% of the Eddington limit. The real M87* and Sagittarius A* are fed far more slowly and glow mainly in radio.
• The Milky Way in the background is procedural. Its stars and dust are generated, not a catalogue.

Keys

← → journey stops · H hide interface · F full screen · P drop a probe · Space pause time (Explore)

Sources

• R. P. Kerr, Gravitational field of a spinning mass, PRL 11, 237 (1963). B. Carter, Global structure of the Kerr family, Phys. Rev. 174, 1559 (1968).
• J. M. Bardeen, W. H. Press & S. A. Teukolsky, Rotating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation, ApJ 178, 347 (1972).
• I. D. Novikov & K. S. Thorne (1973); D. N. Page & K. S. Thorne, ApJ 191, 499 (1974). K. S. Thorne, Disk accretion onto a black hole II, ApJ 191, 507 (1974), the 0.998 spin limit.
• J.-P. Luminet, Image of a spherical black hole with thin accretion disk, A&A 75, 228 (1979), the first such picture, drawn by hand.
• O. James, E. von Tunzelmann, P. Franklin & K. S. Thorne, Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar, CQG 32, 065001 (2015).
• Event Horizon Telescope Collaboration, ApJL 875, L1 (2019) (M87*) and ApJL 930, L12 (2022) (Sgr A*).
• A. C. Fabian et al., A deep Chandra observation of the Perseus cluster, MNRAS 344, L43 (2003), the B-flat.
• J. C. A. Miller-Jones et al., Cygnus X-1 contains a 21-solar mass black hole, Science 371, 1046 (2021). K. El-Badry et al., A Sun-like star orbiting a black hole, MNRAS 518, 1057 (2023).
• S. W. Hawking, Black hole explosions?, Nature 248, 30 (1974).

Part of Beyond Violet, interactive essays on light. Every colour that stands for real light is computed from a spectrum.