Explore an interactive black hole simulator

Trace the lens in three steps

First, place the amber light source in the scene. On a pointer device you can drag it; on a phone you can tap; with a keyboard you can focus the scene and use the arrow keys. Moving the source changes how closely its route approaches the center. Second, select a Compact, Standard, or Deep well mass preset, or use the slider to choose a smaller increment. Third, trace the light. The simulator draws an enhanced path toward the observer and reports a teaching estimate for the bend.

A controlled comparison works best. Change only one variable between runs. Hold the source position steady while increasing mass, or keep mass fixed while moving the source closer to the horizontal centerline. Select replay after a completed run to reset the progress steps. The scene remains interactive throughout, so the experiment is quick enough to repeat several times.

How this black hole simulator works

The model uses normalized geometric units where the gravitational constant G and the speed of light c are set to one. In those units, distances can be expressed as multiples of mass M. Increasing M expands all three reference circles together. The visual light trail responds to the selected mass and the source height, while the numerical readout uses the familiar weak-field teaching estimate α ≈ 4M/b. Here b is an approximate impact parameter describing the ray’s approach.

This formula is valuable for comparing broad trends: more mass produces more bending when the approach is held fixed, and a wider approach produces less bending when mass is held fixed. It is not a full numerical integration of null geodesics. Close to the black hole, the lab switches from pretending to offer precision to naming a qualitative regime such as strong lensing or photon-sphere pass. That boundary keeps the lesson honest and makes the limits of the model visible. The about page documents the lab's scope and authorship.

Read the three landmark radii

The event horizon is marked at 2M. It is the one-way boundary in the Schwarzschild model, and a path that crosses it does not return to the distant observer. The photon sphere is marked at 3M. It describes an unstable circular light orbit, not a solid surface or permanent ring of material. The innermost stable circular orbit, or ISCO, is marked at 6M for massive test particles. It is different from the photon sphere because light and matter do not follow the same kind of orbit.

These circles are reference landmarks, not a literal scale drawing of an astrophysical photograph. Their spacing is mathematically normalized, while their lines, colors, glow, and apparent thickness are artistically enhanced so they remain readable on small screens. The background is visual atmosphere. The overlays and readout carry the teaching information.

What to try on your next run

Begin with the source high in the scene and select 0.8M. Trace once and note the impact parameter, estimated angle, and named regime. Replay, keep the source at the same height, and select 1.3M. The reference radii should expand and the comparison estimate should increase. Next, return to 1.0M and move only the source. A closer approach should reduce b and increase the displayed bend. If a result seems surprising, replay the two cases while changing exactly one control.

A useful final question is not “Does this look dramatic?” but “Which part of the result follows from the normalized relationship?” The 2M, 3M, and 6M values scale directly with mass. The weak-field estimate changes with M and b. The glow, color separation, background nebula, and thickness of a light trail are presentation choices. Separating those layers is part of the experiment.

Questions about the model

Is this black hole simulator scientifically exact?

No. It is a lightweight 2D teaching approximation for a non-rotating Schwarzschild black hole. It does not simulate rotation, accretion plasma, time evolution, telescope optics, or research-grade ray tracing. It also makes no Kerr black hole claim. Normalized distances provide the scientific structure, while trails and color are enhanced for clarity.

What do 2M, 3M, and 6M mean?

They mark the Schwarzschild event horizon, photon sphere, and innermost stable circular orbit in geometric units. Each grows in direct proportion to the mass chosen in the lab.

Does it work on a phone?

Yes. Tap the scene to place the source, choose a mass, and trace the result. The canvas limits pixel density for smooth mobile performance and the controls stack into a single column. The privacy notice explains the optional consent-based aggregate measurement used on this site.