# Kerr Black Hole

[← Back to the gallery index](index.md)

Recipes: `images/create-gallery-images.sh` (checkerboard, blackbody, and
volumetric renders, grid animation), `images/create-vantage-images.sh`
(close vantages), `images/create-main-image.sh` with its
`TEMPERATURE`/`EXPOSURE` overrides (temperature series), and
`scripts/rendering/create_kerr_images.sh` (spin-sweep animations).
Not scripted: the photon-ring pair (6x zoom section renders of the
main-image scene, with the disc removed for the control) and the
trajectory visualization (ray-export plus `scripts/plotting`; see
`scripts/Readme.md`).

### Checkerboard Accretion Disk
<div align="center">
  <img src="render_kerr_large_a_checker_texture.png" alt="Super-extremal Kerr naked singularity (a greater than M): no horizon, no shadow">
  <p>Super-extremal Kerr (a = 0.55 &gt; M): a naked singularity. With no horizon there is no shadow; where the black disc would be, you see light that passed arbitrarily close to the singularity, wound into a chaotic core.</p>
</div>

<div align="center">
  <img src="render_kerr_checker_texture.png" alt="Kerr black hole with a checkerboard accretion disk showing frame dragging and lensing">
  <p>Kerr black hole with a checkerboard accretion disk showing frame dragging and lensing</p>
</div>

### Blackbody Radiation

Two vantages on a Novikov-Thorne blackbody disc: a distant view of the
full system and a close-up where the shadow dominates and the disc wraps
over the top. The pairs differ in disc temperature (8000 K vs 4000 K)
and spin: the red pair sits at a = 0.4995, essentially extremal.

<div align="center">
  <img src="kerr_blackbody_disk_1.png" alt="Kerr black hole with a hot blackbody accretion disk, distant view">
  <p>Hot (8000 K) blackbody disc at a = 0.499, distant view (background image: <a href="https://commons.wikimedia.org/wiki/File:Messier_object_025.jpg">M25</a>)</p>
</div>

<div align="center">
  <img src="kerr_blackbody_disk_2.png" alt="Kerr black hole with a hot blackbody accretion disk, close-up on the shadow">
  <p>The same disc up close: the shadow dominates, the disc wraps over the top, and the approaching side is visibly blueshifted</p>
</div>

<div align="center">
  <img src="kerr_blackbody_disk_a_0_5__1.png" alt="Essentially extremal Kerr black hole with a cool red blackbody disk, distant view">
  <p>Cool (4000 K) blackbody disc at a = 0.4995 (essentially extremal; exactly a = M is degenerate as the ISCO meets the photon orbit), distant view</p>
</div>

<div align="center">
  <img src="kerr_blackbody_disk_a_0_5__2.png" alt="Essentially extremal Kerr black hole with a cool red blackbody disk, close-up on the shadow">
  <p>The extremal-limit disc up close</p>
</div>

### Volumetric Rendering
<div align="center">
  <img src="render_kerr_checker_texture_volumetric.png" alt="Kerr black hole with a checkerboard disk and volumetric rendering of the surrounding medium">
  <p>Kerr black hole with a checkerboard disk and volumetric rendering of the surrounding medium</p>
</div>

<div align="center">
  <img src="render_kerr_stars_volumetric.png" alt="Kerr black hole visualization with background stars and volumetric disc">
  <p>Kerr black hole visualization with background stars and volumetric disc (background image: <a href="https://commons.wikimedia.org/wiki/File:NGC6355_-_HST_-_Potw2301a.jpg">NGC 6355</a>)</p>
</div>

### Accretion-disc temperature series

The main-image scene (see `images/create-main-image.sh`) rendered at three
peak disc temperatures. Lensing and camera are identical; only the
Novikov-Thorne calibration target changes, with `--exposure` compensating
the (T/T_ref)^4 brightness difference so the frames stay comparable.

<div align="center">
  <img src="kerr_disc_temperature_8000k.png" alt="Kerr volumetric disc at 8000 K peak temperature: deep amber, sparse outskirts">
  <p>8000 K (exposure 5): deep amber; the cool outskirts thin toward transparency, stars showing through.</p>
</div>

<div align="center">
  <img src="kerr_disc_temperature_12000k.png" alt="Kerr volumetric disc at 12000 K peak temperature: pale gold, fully luminous">
  <p>12000 K (exposure 1): the previous main-image temperature; pale gold, fully luminous end to end.</p>
</div>

<div align="center">
  <img src="kerr_disc_temperature_20000k.png" alt="Kerr volumetric disc at 20000 K peak temperature: cream white">
  <p>20000 K (exposure 0.13): pale ivory with a blue-white core. At matched brightness the frame is only mildly hotter-looking than 12000 K, because the visible-band blackbody chromaticity converges toward blue-white above ~10000 K; most of what higher temperature buys here is radiance, not color.</p>
</div>

### Photon-ring windings

<div align="center">
  <img src="kerr_photon_ring_windings.png" alt="Nested higher-order images of the volumetric disc winding around the shadow's edge">
  <p>6x zoom onto the shadow's limb (12000 K scene): successive lensed images of the disc wind around the photon ring, each order ~23x thinner than the last (surface brightness is conserved, so each stays at full luminance until it falls below pixel scale; the grainy fringe is every deeper order averaging inside single pixels).</p>
</div>

<div align="center">
  <img src="kerr_critical_curve_starfield.png" alt="The same crop with the disc removed: the bare critical curve against wound starlight">
  <p>The control: the identical crop with the disc removed. The smooth boundary is the critical curve (its long straight stretch is the near-extremal "D-shape" flattening of the prograde limb at a/M = 0.998), and the faint concentric striations hugging it are the photon ring itself with only starlight as its source. Every winding in the image above slots into this scaffolding; same geometry, hot gas instead of faint stars as the paint.</p>
</div>

### Animations
<div align="center">
  <img src="kerr_animation.gif" alt="Animation of a spinning Kerr black hole with a rotating accretion disk">
  <p>Animation of a spinning Kerr black hole with a rotating accretion disk</p>
</div>

<div align="center">
  <img src="kerr_animation_stars_and_disk.gif" alt="Animation of a Kerr black hole with background stars and a rotating accretion disk">
  <p>Animation of a Kerr black hole with background stars and a rotating accretion disk (background image: <a href="https://commons.wikimedia.org/wiki/File:Messier_object_025.jpg">M25</a>)</p>
</div>

### Close vantages

First-person views near the near-extremal hole (a = 0.499, ZAMO
observer; recipes: `images/create-vantage-images.sh`). The first four
placements mirror the [Schwarzschild series](schwarzschild.md#close-vantages);
frame dragging pulls every one of them into asymmetry. The disc glow is
3500 K gas, blueshifted by the deep gravity well.

<div align="center">
  <img src="vantage_kerr_dragged_porthole.png" alt="The sky porthole near the Kerr horizon, dragged into asymmetry">
  <p>Dragged porthole (just outside the horizon, looking straight out): the Schwarzschild porthole again, but frame dragging squeezes the sky circle off-axis and the plunging inner disc glow floods in from the sides.</p>
</div>

<div align="center">
  <img src="vantage_kerr_photonsphere_edge.png" alt="The Kerr winding wall over bright inner-disc glow">
  <p>Photon-shell edge, hovering just above the disc surface: the winding wall of stacked disc and sky images, with the glowing surface curving away beneath the camera.</p>
</div>

<div align="center">
  <img src="vantage_kerr_grazing_winding.png" alt="Grazing multiple windings around the Kerr hole">
  <p>Grazing view, skimming just above the disc surface inside its annulus: the multiple-winding band, distorted relative to Schwarzschild because prograde and retrograde light circle at different radii around a spinning hole.</p>
</div>

<div align="center">
  <img src="vantage_kerr_rearview.png" alt="Looking away from the Kerr hole at sky and disc">
  <p>Rearview: the magnified outward sky and the disc band, the near-side gas brightened by Doppler beaming.</p>
</div>

<div align="center">
  <img src="vantage_kerr_ergosphere_prograde.png" alt="Looking prograde from inside the ergosphere">
  <p>Inside the ergosphere, looking prograde (the direction spacetime itself rotates): the winding wall seen from a region where standing still relative to the stars is impossible.</p>
</div>

<div align="center">
  <img src="vantage_kerr_polar.png" alt="The shadow seen from the rotation axis, circular despite near-extremal spin">
  <p>From the rotation axis, facing the hole: the disc face-on behind a shadow that stays circular; pole-on, even near-extremal spin barely distorts the silhouette, in contrast to every equatorial view.</p>
</div>

<div align="center">
  <img src="vantage_kerr_gap_rim.png" alt="View from inside the gap between disc and horizon, toward the rim">
  <p>From inside the gap between the disc's inner edge and the horizon, looking back along the orbit: the wound images pile up against the rim of the shadow.</p>
</div>

<div align="center">
  <img src="vantage_kerr_gap_outward.png" alt="Looking outward from inside the disc gap">
  <p>The same spot, looking straight out: the sky and outer disc compressed into an oval by the gravity of the hole behind the camera.</p>
</div>

### Trajectories
<div align="center">
  <img src="kerr_trajectory_near_horizon.png" alt="Visualization of a ray trajectory approaching the event horizon of a Kerr black hole">
  <p>Visualization of a ray trajectory approaching the event horizon of a Kerr black hole</p>
</div>
