SCIENTIFIC PREVISUALIZATION

Photon sphere light that orbits

Each pixel traces a light ray — a “null geodesic” bent by gravity. You see the thin photon ring and the flat disk lensed above and below the shadow.

MetricSchwarzschild + spin Doppler

DiskThin Keplerian
T ∝ r−3/4

Shadow~5.2 Rs lensed

Mass0.76

Spin0.625

Temperature1.23

Film0.15

Horizon r+

Photon ring

ISCO

Shadow diam

Anatomy of the lensed image

Seen nearly edge-on (80°), the same flat disk appears below the shadow in front and arched above it behind — light bent by gravity. The side spinning toward you looks brighter and whiter.

Horizon

Shadow is not pure black

Faint warm glow inside, brightest along the lower-left edge where hot gas skims the horizon.

Photon sphere

Razor photon ring

A razor-thin ring where light circles the hole before escaping — brightest where motion blueshifts it.

Doppler

Relativistic beaming

Gas coming toward you is beamed and looks whiter; gas moving away looks dimmer and redder.

Lensing

Lensed above and below

Front of the disk below the shadow; far side bent over the top; a second, lensed image tucked underneath.

Frame drag

Frame-dragged shear

Spin drags space itself, shearing the disk into streaks.

Per fragment Schwarzschild null integration

d2p dlambda2 = -3/2 h2 p / r5, Binet u'' = -u + 3/2 rs u2. Velocity-Verlet with angular sweep, bendC continuous via sub-Verlet.

h = cross(p,dir) h2 = dot(h,h)

Conserved, b approx sqrt h2.

dl = min(DLMAX, DPHI r2 / h, 0.35r)

Constant angular step, dphi = dl h / r2.

q = vec3(dRot·2.1, log r·12.5) d=norm(xz)

Cylindrical embedding, periodic by construction, no atan seam.

I = (3/r)^3.4 inner outer striate bright

Thin-disk, tau, alpha, grazing guard.

bendC = bend - dBend·(1-s) + 4x sub-Verlet

Interpolate to event time, remove step quantization lines.

glow = 0.196 0.158 0.104 * (0.042+0.098 rimG lobe)

Shadow interior warm olive.