Ergosphere — A Kerr observatory

01 SPACETIME

PROGRADE

Spin a*0.00 Inclination i38°

INNER EDGE 6.00 GM/c² · ISCO

02 THE CLOCK EXPERIMENT

MM:SS · 60×

∞ DISTANT OBSERVER

00:00.0

1.000×

PROBE P–01

00:00.0

0.791×

Δτ 0.0 s

03 OBSERVATION

GUIDED

Above the accretion disk

A real geometry.
An interpreted light.

A Kerr black hole with a thin, prograde disk. This is a physically informed observatory, not an exact image of an astrophysical black hole.

DIMENSIONLESS SPIN0.00 a*

VIEWING INCLINATION38.0 deg

PROGRADE ISCO6.00 GM/c²

EVENT HORIZON2.00 GM/c²

EXACT MODEL Shadow, edge & orbits

The shadow boundary follows the Kerr critical curve for a distant observer, computed from unstable spherical photon orbits. It is not the event horizon. Spin shifts and flattens the shadow.

The disk ends at the prograde innermost stable circular orbit: 6 GM/c² at a* = 0, and about 1.45 GM/c² at a* = 0.99. The horizon is r₊ = 1 + √(1 − a*²).

UNLENSED RADIAL COORDINATE

Horizon 2.00ISCO 6.00 GM/c²

HYBRID How the light is bent

Schwarzschild null rays are numerically integrated into a lookup table, including multiple disk crossings. Their impact parameters are remapped to the Kerr critical curve; a radial remapping matches the Kerr horizon and photon-orbit radii.

This brings the far side above and below the shadow, but is not full Kerr ray tracing. Photon frame dragging, travel-time delays and returning radiation are not solved.

u″ + u = 3u² · u = 1/r
The Schwarzschild null-ray equation, in G = c = M = 1.

DISPLAY MODEL Heat, motion & redshift

A zero-torque, Newtonian thin-disk profile sets the heat: T ∝ [r⁻³(1 − √(r_ISCO/r))]^¼. It is normalized across spin for a readable comparison, rather than a full Novikov–Thorne disk.

At each approximate emission point, the Kerr circular-orbit frequency shift is g = 1 / [u^t(1 − Ωλ)], with λ = −α sin i. This includes gravitational redshift and orbital Doppler shift. The approaching side is brighter and bluer.

Bolometric brightness is weighted by g⁴. A display palette follows gT; it is not a calibrated spectrum. Exposure is gently normalized across spin. Turbulence, bloom and a broadened photon ring are illustrative. The nearly edge-on disk has a small angular floor for visibility; stars use an illustrative weak-field warp.

EXACT RATE One orbit. Two clocks.

The probe follows a stable circular equatorial geodesic at the displayed radius. The distant clock measures coordinate time t; the probe accumulates its own proper time τ.

Ω = 1 / (r^3/2 + a*)
dτ/dt = √(1 − 3/r + 2a*/r^3/2) / (1 + a*/r^3/2)

The rate includes gravity and orbital motion. Inclination changes the image, not the clock rate. This is not the rate at which delayed light pulses would reach the camera.

The mass is 10⁶ solar masses; GM/c³ = 4.9255 seconds. Both clocks and orbital motion run at 60 simulated seconds per real second. The probe marker and its direct-image orbit guide are enlarged for inspection.

Changing spin or moving the orbit compares quasi-static models, not a physical spin-up or a thrust maneuver. The probe is kept at least 0.25 GM/c² outside the ISCO.

All radii use GM/c², not kilometres.
i = 0° is pole-on; 90° is edge-on.
Continue to 180° to orbit below the disk.

At the controls

Orbit · Zoom · Pan: Drag, use the scroll wheel, or shift-drag. On touch screens, drag to orbit, pinch to zoom, and use two fingers to pan.
Keyboard, after clicking the scene: Arrow keys orbit · + / − zoom · Space pauses time
R resets the camera · L toggles labels · H hides instruments

GEOMETRY: Kerr (1963); Bardeen, Press & Teukolsky (1972).
Critical-curve construction and equatorial circular geodesics.
VISUALIZATION: procedural emission + hybrid ray-transfer lookup.

The shape of
darkness.

A clock in free fall.

The shape ofdarkness.

A clock in free fall.

The shape of
darkness.