Ray-traced black hole simulation

A black hole bends the light from everything around it. Rendering one properly means tracing each light ray backwards through curved spacetime, and that is what this simulation does for every pixel, in real time.

Interactive, free and runs in your browser. Part of the Frontier Physics simulations.

What you will see

The dark shadow sits inside a glowing accretion disc. Light from the far side of the disc is bent over the top and under the bottom of the shadow, so you see the back of the disc as an arch. The side of the disc moving towards you is brighter because of Doppler beaming, and the stars behind are lensed into arcs near the edge.

Try this

  1. Orbit the camera to a low angle and watch the far side of the disc arch over the shadow.
  2. Find the thin bright ring hugging the shadow: light that looped around the hole.
  3. Change the mass and see the whole scene scale with the Schwarzschild radius.

Common misconception

The black shadow is not the size of the event horizon. Gravity bends light around the hole, so the shadow appears about 2.6 times the Schwarzschild radius across, larger than the horizon itself.

Exam-style question

What are the event horizon and photon sphere radii for a black hole of 10 solar masses?

r_s = 2GM/c² ≈ 2.95 km per solar mass, so about 29.5 km. The photon sphere is at 1.5 r_s ≈ 44 km.

Key equations

  • r_s = 2GM / c²
  • r_ph = 1.5 r_s
  • b_crit = (3√3/2) r_s

Curriculum

IB Physics E.5, enrichment: astrophysics and cosmology.

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