Interactive relativistic black hole accretion disk visualization with Doppler beaming, gravitational redshift, and thin-disk temperature profile T(r) ∝ r⁻³ᐟ⁴
Matter falling toward a black hole forms a thin, rotating disk due to conservation of angular momentum. Viscous dissipation (turbulence, magnetic stresses) converts orbital energy to thermal radiation. The standard Shakura-Sunyaev (1973) model gives the temperature profile T(r) ∝ r⁻³ᐟ⁴ outside the ISCO, with the peak temperature occurring slightly outside the inner edge rather than exactly at the ISCO. The disk luminosity can reach up to ~10% of the rest mass energy (η ≈ 0.1 for Schwarzschild, ~0.42 for maximal Kerr spin), far exceeding nuclear fusion (η ≈ 0.007).
Three key relativistic effects shape the observed appearance: (1) Projected disk geometry and light-bending-inspired near/far-side overlap create the compressed ring-like view at high inclination. (2) Doppler beaming brightens the approaching side and dims the receding side (relativistic aberration × Doppler shift). (3) Gravitational redshift dims light emitted deep in the potential well. This demo is a teaching-oriented approximation, not a full general-relativistic ray tracer, but it captures the main brightness asymmetry seen in black-hole images such as M87* (2019) and Sgr A* (2022).
Accretion disks are observed across the mass spectrum: (1) X-ray binaries (stellar BH, ~10 M☉) in our Galaxy — the iron Kα line at 6.4 keV shows relativistic broadening from disk reflection. (2) Active Galactic Nuclei (supermassive BH, 10⁶-10⁹ M☉) — the big blue bump in UV/optical continuum from thermal disk emission. (3) Tidal disruption events — a star torn apart by a supermassive BH produces a transient bright flare. (4) The Event Horizon Telescope has directly resolved the shadow and ring for M87* and Sgr A*, confirming GR predictions.
The main panel shows a relativistic teaching visualization of the accretion disk around a black hole. The bright crescent on one side is caused by Doppler beaming (approaching gas is boosted), while gravitational redshift suppresses the innermost emission. Adjust the inclination to see how the view changes from face-on (nearly circular and symmetric) to edge-on (compressed and more asymmetric). Change the black hole mass to see how temperature and luminosity scale. Increase the spin parameter to shrink the ISCO and produce a hotter, more compact disk. The temperature plot shows T(r) ∝ r⁻³ᐟ⁴ outside the ISCO, and the spectrum panel shows the multi-temperature blackbody emission.