Black hole simulation

Interactive Schwarzschild gravitational lensing

Interactive black hole simulation

This browser-based black hole simulation visualizes a non-spinning Schwarzschild black hole with gravitational lensing, a luminous accretion disk, photon ring cues, relativistic Doppler color shift, redshift, bloom, and an optional fall mode that approaches and crosses the event horizon.

The simulation is designed for physics education, astronomy learning, and general relativity visualization. It runs in WebGL 2 and explains the modeled equations, parameters, approximations, and limitations in the physics information panel.

Drag: orbit · Shift drag: move
Wheel or pinch: zoom

Physics model

What is simulated, what is visualized, and what is simplified.

Equations Used

Schwarzschild spacetime
ds2 = - ( 1- rsr ) c2 dt2 + ( 1- rsr ) -1 dr2 + r2 dΩ2
Null rays
ds2 = 0 Light follows null geodesics; disk intersections use a precomputed Schwarzschild bending table.
Photon-sphere critical curve
rph = 32 rs , ecrit = 427
Doppler factor approximation
g ≈ ggrav γ (1-βμ) , γ = 1 1-β2
Relativistic brightness
I ν,obs ≈ g3 I ν,emit
Free-fall observer mode
βff = rsr , μ′ = μ+β 1+βμ

Simulation Parameters

Black hole type
Schwarzschild: non-spinning and uncharged.
Spin
Dimensionless spin a* = 0. Kerr frame dragging is not simulated.
Physical mass
No mass is assigned. The scene is scale-free; choosing any mass M sets r_s = 2GM/c² and scales every length with r_s.
Horizon radius
r_s = 0.5 renderer units.
Photon sphere
r_ph = 1.5 r_s = 0.75 renderer units.
Disk inner edge
3 r_s = 1.5 renderer units, matching the Schwarzschild ISCO.
Bright disk edge
5.6 r_s = 2.8 renderer units.
Default observer
14.4 r_s = 7.2 renderer units from the black hole.
Free-fall trajectory
The fall mode advances a radial geodesic dropped from rest at infinity. The simulated observer crosses r_s; the exterior renderer samples at about 1.0015 r_s during the interior handoff to avoid the Schwarzschild coordinate singularity, and the post-horizon display clock is stretched so crossing does not look like a hard cut before the final fade toward the singularity.
Disk Doppler speed
Approximate visual orbital speed β ≈ 0.44, used for the screen-continuous Doppler color and brightness shift.

Modeled For The Visual

  • Non-spinning Schwarzschild black-hole lensing and shadow geometry.
  • Primary and secondary accretion-disk images from solved ray paths.
  • A faint critical-curve cue for unresolved higher-order disk images.
  • Approximate gravitational redshift, Doppler color shift, and g³ beaming.
  • Free-fall view aberration and a proper-time horizon crossing.

Simplified Or Not Included

  • No Kerr spin, frame dragging, tilted disk, or asymmetric Kerr shadow.
  • No physical mass, accretion rate, temperature, or telescope distance is assigned.
  • The disk Doppler field is screen-continuous, not a full per-ray emitter four-velocity solve.
  • Interior rendering uses a causal light-cone compression visual, not full null geodesics in horizon-regular coordinates.
  • The higher-order photon ring is a faint critical-curve cue, not a full sum of all orbiting images.
  • No radiative transfer, absorption, polarization, magnetic fields, or plasma simulation.
  • The accretion disk texture, glow, and turbulence are procedural visual materials.
  • Camera exposure, bloom, and tone mapping are artistic display choices.