Real-Time Relativistic Simulation

Where Even Light Cannot Escape

A real-time, physics-based educational visualization of light around a Schwarzschild black hole. Every frame is computed on your GPU by numerically tracing light paths through curved spacetime — the bending, the shadow and the bright rim arise from those paths.

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Light Does Not Travel Straight

The upper arch and the lower ring are lensed images of the disk's far side, traced ray by ray through curved spacetime. Direct disk light is temporarily suppressed here to make the traced lensed images easier to see — the geometry itself comes from the ray tracing alone, and nothing is amplified.

Light Near the Critical Orbit

Surrounding disk light is dimmed here for visibility. The bright rim hugging the shadow is light on near-critical paths — rays that loop around the black hole before escaping. The critical impact parameter is bc = (3√3/2) rs ≈ 2.598 rs; rays inside it fall through the horizon. The infinite stack of higher-order subrings is real, but far below display resolution.

The Approaching Side Blazes

Inner disk material orbits at up to half the speed of light. The total frequency shift combines Doppler and gravitational redshift, g = νobsem = √(1−rs/r)·√(1−v²)/(1−v·μ), and observed intensity scales as g⁴ (bolometric approximation). The approaching side brightens toward white, the receding side reddens — this scene changes only framing and exposure; the beaming itself is never exaggerated.

Gravity Has the Final Word

The disk's inner edge marks the innermost stable circular orbit — the Schwarzschild ISCO at 3 rs. Inside it no stable circular orbit exists. Rotation follows Kepler's law, Ω ∝ r−3/2; playback speed is raised in this scene so the differential shear is visible to the eye.

The Event Horizon in Numbers

3 rs
ISCO radius
2.598 rs
Critical impact parameter
~0.5c
Inner edge velocity
α ≈ 2rs/b
Weak-field deflection

How It Works

This page renders the accretion disk around a black hole under the rules of general relativity, entirely in your browser. For every pixel, a light path is numerically integrated backwards through the Schwarzschild metric; each point where the path crosses the disk plane contributes emission according to the local temperature and frequency-shift factor.

The disk's rotation follows Kepler's law, the brightness asymmetry comes from relativistic Doppler beaming combined with gravitational redshift, and colors use a blackbody-inspired temperature mapping over a simplified thin-disk profile. The disk texture is procedural turbulent structure advected with the Keplerian flow. The visual composition is inspired by NASA Goddard's 2019 black hole visualization.

Note: Accretion disks can radiate across optical, ultraviolet and X-ray wavelengths; their spectrum and temperature depend strongly on black-hole mass and accretion state. Orbital periods scale with mass as well — from milliseconds around stellar-mass black holes to hours or days around supermassive ones. Speeds and colors here are scaled for the human eye.

Method & Limits. This is a physics-based educational visualization using numerically traced light paths in Schwarzschild spacetime (a non-rotating black hole), a geometrically thin accretion disk, and a simplified zero-torque thin-disk temperature model with blackbody-inspired colors. Disk texture is procedural turbulence advected with the Keplerian flow; display colors, exposure and rotation speed are visualization choices. The first-order integrator reproduces the critical impact parameter to about 1% and the photon-sphere approach to a few percent. It is not a GRMHD simulation and not a full general-relativistic radiative-transfer model.