WARPLAB

What am I looking at?

What you are looking at

A black hole's picture, traced ray by ray through curved space-time: the dark shadow, the thin photon ring round it and a glowing disk of gas bent over the top. Set the mass, spin and viewing angle, then open EHT images to put the Event Horizon Telescope's real pictures of M87* and Sgr A* beside the model at the same scale.

Controls

On this device:

Mouse

  • Drag the picture to orbit round the hole; scroll to move closer or farther. Orbit, Closer, Farther and Reset view do the same.
  • Click M87* or Sgr A* to take that hole's mass and distance; drag Mass, Spin and Viewing angle.
  • Click Accretion disk, Photon ring, Shadow outline, ISCO and Sky grid to show or hide each one.
  • Click EHT images to compare. Blur to 20 µas matches the telescope's sharpness; Mass from the paper puts the published mass back.
  • Click the badge beside a number from the papers for its source and licence.

Keyboard

  • Tab to Orbit, Closer, Farther or Reset view and press Enter or Space to move the camera.
  • Tab to a slider; the arrow keys move it, Home and End jump to its ends.
  • On the tabs, the left and right arrows switch between The black hole and EHT images.
  • H or ? opens this panel. Esc closes it.
Other devices

Touch

  • Drag the picture with one finger to orbit; pinch with two to move closer or farther.
  • Tap a source, then slide Mass, Spin and Viewing angle.
  • Tap a layer button to show or hide it.
  • Tap EHT images; on a phone the two pictures stack, the EHT's on top.

Headset and AR

  • On a headset, Enter VR stands you 10 Schwarzschild radii from the hole, which fills the angle it really would: about 28°.
  • Point a controller or your hand at the panel. Pull the trigger or pinch to press.
  • Panel: Closer and Farther (5 to 20 Schwarzschild radii), Spin and Tilt up or down, Disk on or off, Start again. It reads out the shadow's angle and how fast your clock runs.
  • Aim at the floor and press to teleport; the right stick turns 30° at a time. Exit VR is on the panel.
  • The first session opens a short intro that teaches these controls; Controls on the panel opens it again.

Glossary

Black hole
A region where gravity is so strong that nothing, not even light, gets back out. Its boundary is the event horizon.
Why it matters Every picture here is of the light round it: the hole itself gives none.
GM/c²
The natural length of a black hole of mass M: 1.5 km for the Sun's mass, 64 AU for M87*. Every distance in the model is measured in it, so one picture fits any mass.
Event horizon
The surface of no return, at r₊ = (1 + √(1 − a²)) GM/c²: 2 GM/c² (the Schwarzschild radius) with no spin, down to 1 GM/c² at the fastest spin.
Spin a
How fast the hole turns, from 0 to just under 1. A spinning hole drags space round with it, so orbits and light on one side differ from the other.
Why it matters The EHT and simulations favour a fast spin for M87*, near 0.9.
Shadow
The dark patch where light would come from the hole's direction but none can: rays aimed there fall in. With no spin it is 2√27 ≈ 10.4 GM/c² across, 2.6 times the horizon.
Why it matters Its size depends almost only on mass over distance, so it weighs the hole.
Photon ring
Light that went round the hole once or more before reaching you, piled into a thin ring at the shadow's edge. The Photon ring layer lights the disk's light that crossed its plane before landing.
Photon sphere
Where light can orbit, unstably: 3 GM/c² with no spin. Rays that skim it can wind round many times; seen from far away its edge is the shadow's, √27 GM/c² from the centre.
Innermost stable circular orbit (ISCO)
The closest circular orbit that lasts: 6 GM/c² with no spin, 1 GM/c² at the fastest. Gas inside it plunges in, so the disk ends there.
Why it matters How deep the disk reaches sets how much energy it can release: 6% of its mass with no spin, up to 32% spinning fast.
Accretion disk
Gas orbiting the hole in a thin, flat disk, heated by its own friction as it spirals in. The model uses the Novikov–Thorne disk, with the Page–Thorne formula for the light from each ring.
Doppler beaming
Gas coming towards you looks brighter and bluer, gas going away dimmer and redder. At a third of light speed the difference is more than tenfold.
Gravitational redshift
Light climbing out of a deep well loses energy. Together with beaming it sets g, the ratio of the light's energy here to its energy at the gas; brightness goes as g⁴.
Gravitational lensing
Gravity bending light. Near the hole it bends so much that the far side of the disk shows over the top of the shadow, and the sky behind is stretched into rings: the Sky grid layer shows it.
Viewing angle
The angle between your line of sight and the spin axis: 0° looks down on the disk, 90° along its edge. M87*'s jet points about 17° from us.
Microarcsecond (µas)
A millionth of a second of arc: the width of a doughnut on the Moon, seen from Earth. M87*'s ring is 42 µas across.
Why it matters Seeing it took telescopes spread over the Earth, working as one dish the planet's size.
θg
GM/c² seen from Earth: GM/(c²D) as an angle. The ring is about 11 θg across; the papers give 3.8 µas for M87* and 4.8 µas for Sgr A*.
Event Horizon Telescope (EHT)
Radio telescopes on several continents observing together at 1.3 mm, combined by very long baseline interferometry. Its resolution is about 20 µas.
Why it matters Its 2017 campaign gave the first images of a black hole's shadow: M87* (released 2019) and Sgr A* (2022).
Resolution (beam)
The smallest detail the array can see, about 20 µas: images are blurred by a spot that size. The circle in the corner of each picture shows it.
Ring diameter
The emission ring's size, measured from the brightest radius round a centre chosen to make it the same in every direction (the EHT's REX method). Blurring pulls it inwards a little.
Hawking temperature
Quantum theory gives every black hole a faint glow at T = ħc³/(8πGMk_B): 6 × 10⁻⁸ K for one solar mass, colder for heavier ones, zero at the fastest spin.
Why it matters M87*'s is about 10⁻¹⁷ K, far below the 2.7 K of the cosmic background: it absorbs more than it emits.
Kerr space-time
The exact solution of Einstein's equations for a spinning black hole (Roy Kerr, 1963). The picture traces light through it; with no spin it is Schwarzschild's.
Ray tracing
Following each pixel's light backwards, step by step along its curved path, until it falls in, hits the disk or reaches the sky. The web view does it on the graphics card; the headset reads the bends from a precomputed table.

All help and questions

A black hole's shadow

Trace light round a spinning black hole: the shadow, the photon ring and the bent disk. Compare it with the EHT's real images.

Drag the picture to orbit; scroll or pinch to move closer.

Source

Sets the size, the shadow's angle from Earth and the temperature, never the shape. M87* weighs 6.5 × 10⁹ M☉.

0 is a Schwarzschild hole; near 1 the hole drags space round with it, the disk reaches closer in and the shadow flattens on one side.

Degrees between your line of sight and the spin axis: 0° looks down on the disk, 90° along its edge. M87*'s jet says about 17°.

Show
Horizon radius
120 AU
1.87 GM/c²
Shadow across, seen from Earth (M87*)
39.4 µas
10.31 GM/c²
Hawking temperature
8.8 × 10⁻¹⁸ K
Innermost stable orbit
272 AU
4.23 GM/c²
Camera distance
30 GM/c²
15.0 Schwarzschild radii

In units of GM/c² the picture is the same for any mass: mass only scales it.

The shadow

Light that passes closer than √27 ≈ 5.2 GM/c² from the centre spirals in and never comes out. The dark patch it leaves, the shadow, is 2√27 ≈ 10.4 GM/c² across: 2.6 times the horizon. Spin squashes one side of it, by a few per cent.

The disk

Gas orbits in a thin disk down to the innermost stable orbit and glows from the heat of its own friction (Novikov and Thorne). The side coming towards you looks brighter and bluer, the side going away dimmer: Doppler beaming. Gravity bends the far side's light over the top of the shadow and under it.

How the picture is made

Each pixel's light ray is traced backwards through the Kerr space-time, a few hundred steps at a time, until it falls in, lands on the disk or reaches the sky. The same tracer, run in the tests, matches Bardeen's shadow outline within 0.2%.

Credits

EHT images: Event Horizon Telescope Collaboration, First M87 EHT Results I (ApJL 875, L1, 2019, CC BY 3.0) and First Sgr A* EHT Results I (ApJL 930, L12, 2022, CC BY 4.0), Figure 3 of each, with the papers' ring diameters, masses and distances.

Shadow outline after Bardeen (1973); light bending in closed form after Darwin (1959); the disk after Novikov and Thorne (1973) and Page and Thorne (1974); the ring measurement after Chael et al. (2019).

M87* paper (2019)Sgr A* paper (2022)Page and Thorne (1974)