Demo Lab

Black Hole Playground

Explore how mass and spin set the scale of a Kerr black hole and its innermost stable orbit, while viewing angle changes the simplified Doppler-brightness contrast of the disk.

The readouts use general-relativistic Kerr equations for an ideal prograde equatorial orbit. The 3D scene is an educational illustration, not a real-time ray trace.

Horizon diameter 180.3 km
Prograde ISCO 4.54 r_g
ISCO clock ratio 1.60×
ISCO grav. redshift z = 0.34
Disk brightness contrast 13.5×
Observable appearance
Conceptual diagrams
Dynamical spacetime
Rendered approximation Accretion disk

A simplified view of hot orbiting material, Doppler asymmetry, the black-hole shadow, and secondary lensed disk images.

Drag horizontally to orbit. Drag vertically—or use Observer angle—to change inclination.
a* is dimensionless: 0 is non-rotating; 0.99 is rapidly rotating. 0° is face-on from above, 90° is edge-on, and 180° is face-on from below. Use this slider or drag vertically; horizontal dragging changes azimuth.
Starting local 3D renderer…

In rotatable modes, drag the scene or use the arrow keys. Press Home to reset the view.

Doppler-brightened side receding, dimmer side photon ring lensed disk image

Mass sets physical scale

One gravitational radius is GM/c². Increasing mass enlarges the horizon and ISCO in kilometers, but does not change their dimensionless radii.

Spin moves the ISCO

The prograde Kerr ISCO contracts from 6 r_g at zero spin toward the horizon as spin approaches its theoretical limit.

Readouts share one reference

Clock ratio and gravitational redshift are evaluated at the prograde ISCO. They are model quantities relative to a distant observer, not measurements of a particular real disk.

Angle changes appearance

The brightness ratio uses a simplified special-relativistic Doppler estimate. Exact images require ray tracing, radiative transfer, and a physical accretion-flow model.