Black Hole Observatory

Every pixel traces a photon backwards through curved spacetime. Orbit the hole, fall into it, or spin it up.

Observer

Camera distance 30 r_s

Black hole & disc

Mass 10 ×10⁶ M☉ Spin a/M 0.00 Disc inclination (tilt) 0° Disc brightness 1.0

Inner r 3.0 Outer r 14

Inner edge at the ISCO (follows spin)

View & quality

Field of view 50° Quality High Time rate 1× Dynamic resolution (holds ~30+ fps)

Render scale —

Orbiting star

Orbit radius 7.0 r_s

Near the hole it is stretched into a glowing tidal stream, and gravity lenses it into multiple images.

Live readouts

Radius r: —
Clock rate √(1−r_s/r): —
Redshift 1+z: —
Circular orbital period: —
Tidal stretch (2 m body): —
Proper time τ: —
Distant observer t: —

Physics of this hole

Schwarzschild radius r_s = 2GM/c²: —
Event horizon r₊: —
Photon sphere: —
Shadow (critical impact b): —
ISCO: —
Period at ISCO: —

What am I seeing?

Ray tracing. For each pixel a photon is followed backwards from the camera. In Schwarzschild spacetime its path obeys d²u/dφ² = −u + (3/2) r_s u² (u = 1/r), which is integrated here as a Cartesian acceleration a = −(3/2) r_s h² x / r⁵ with a Runge–Kutta 4 step that shrinks near the hole.
Shadow. Light is captured inside the photon sphere at 1.5 r_s. Rays with impact parameter below b = 3√3/2 r_s ≈ 2.6 r_s fall in, so the dark disc is about 5.2 r_s wide from far away, much larger than the horizon itself.
Einstein ring & photon ring. Stars behind the hole are smeared into rings. Light that loops once or more around the photon sphere gives thinner and thinner nested images.
The disc. Its far side is bent over the top and under the bottom of the hole (the secondary image). Gas orbits at nearly the speed of light, so the approaching side is Doppler-beamed: brighter and bluer. Gravitational redshift dims and reddens light climbing out of the well, most strongly near the inner edge.
Spin. With spin a the horizon shrinks to (1+√(1−a²))/2 r_s and the ISCO moves inwards for co-rotating orbits. Kerr is modelled with a Lense–Thirring frame-dragging term added to the photon acceleration. This is an approximation, not the full Kerr geodesic.
Fall in. The camera follows a radial free-fall geodesic, d²r/dτ² = −GM/r². Your proper time τ ticks on normally, but a distant observer sees the clock slow and never watch you reach r_s. Tidal stretching grows as 1/r³. Past the horizon the view cannot be shown, so the picture dims.
Circular orbit. Stable circular orbits exist only outside the ISCO at 3 r_s (non-rotating). Between 1.5 and 3 r_s orbits are unstable.
Educational model: disc emission is a stylised thin disc with a Novikov–Thorne-like temperature profile, and the camera is idealised. Time units scale with the chosen mass (r_s/c ≈ 9.85 µs per solar mass).

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