Fly around a black hole whose image is calculated, not painted: every pixel follows a ray of light through curved spacetime, so the disc, the rings and the shadow appear exactly where general relativity puts them.
How to use the black hole simulator
Drag to orbit the black hole and scroll or pinch to move closer or farther away. The views on the left jump to classic angles: edge on shows the disc's far side arching over the black hole, from above shows the disc face on with the shadow in the middle, and close up fills the sky with bent starlight. Fall in carries you down toward the black hole.
The buttons at the top switch parts of the physics on and off so you can see what each one does:
- Disc hides the glowing gas so you see the shadow and the lensed Milky Way alone.
- Doppler turns off the brightening and blueing of the gas coming toward you.
- Lensing makes light travel in straight lines, as it would without gravity. Compare the two and the size of the effect is startling.
Choose a black hole to change the real-world scale in the panel: a 10-solar-mass stellar black hole, Sagittarius A* at the centre of our galaxy, or M87*, the first black hole ever photographed. The picture looks the same for all three, because a non-rotating black hole's appearance scales with its size. The numbers change: the event horizon, the innermost stable orbit, how long an orbit there takes, and how slowly your clock runs.
What you are seeing
The shadow. The dark centre is not the event horizon itself but the black hole's shadow. Any light that passes closer than about 2.6 Schwarzschild radii is captured, so the shadow appears about two and a half times wider than the horizon.
The photon ring. Just outside the shadow, light can loop around the black hole once, twice or more before escaping. Each loop makes a thinner, fainter copy of the whole scene, stacked into bright rings at the shadow's edge.
The disc. Gas spirals in and heats up as it goes. Its temperature peaks just outside the innermost stable circular orbit, three Schwarzschild radii from the centre, where the gas moves at half the speed of light. Inside that, gas plunges straight in, so the disc has a sharp inner edge. The turbulence in the disc shears as it turns, because the inner gas orbits faster than the outer gas.
The arch. Light from the part of the disc behind the black hole is bent over the top and under the bottom, so you see the far side of the disc as a bright arch, the image made famous by the film Interstellar.
The sky. Behind the black hole, the Milky Way is warped into arcs and, where it lines up exactly, into an Einstein ring.
The physics
A non-rotating black hole of mass M has an event horizon at the Schwarzschild radius, rs = 2GM/c². For light, Einstein's equations reduce to one orbit equation, u″ + u = (3/2) rs u², where u is one over the distance from the centre. The simulator writes that equation in Cartesian form and integrates it for one ray per pixel, starting at the camera and running backward in time, until the ray falls into the horizon, escapes to the distant sky, or crosses the disc.
Where a ray crosses the disc, the colour comes from the gas temperature and two shifts. The gravitational redshift factor, √(1 − rs/r), dims light climbing out of the well. The Doppler shift, 1/[γ(1 − β cos θ)], brightens and blues gas moving toward the camera. Brightness scales as the fourth power of the combined shift, so the approaching side can outshine the receding side several times over.
How we check it
The ray tracer's equation and step rule are tested every time the site is built, using the same code in JavaScript:
- The capture threshold, which sets the shadow's size, lands within 1% of √27/2 rs.
- Rays that skim the threshold circle the photon sphere at 1.5 rs.
- Far from the hole, light bends by 2rs/b, the deflection Eddington measured during the 1919 solar eclipse, to within 1%.
- Gas at the innermost stable orbit moves at exactly half the speed of light, and a clock there runs at √(2/3), about 82%, of the far-away rate.
Limits
This black hole does not spin. A spinning (Kerr) black hole, which most real ones are, has a slightly flattened, off-centre shadow and a disc that reaches closer in. The disc is thin and its colours represent relative temperature. Your camera hovers in place, so its own motion does not distort the view, as a falling camera's would.
Questions
Is this what a black hole really looks like?
It is what a non-rotating black hole with a thin, bright disc looks like to a camera hovering nearby. The paths of light are calculated from Einstein's equations for every pixel, so the bending, the shadow and the rings are physically placed. The disc's colours show its relative temperature rather than a precise spectrum, and real discs, like those imaged around M87* and Sagittarius A*, are often thicker, dimmer or partly hidden by gas.
Why is one side of the disc brighter?
The gas orbits at up to half the speed of light. On the side moving toward you its light is squeezed to shorter, bluer wavelengths and beamed forward, so it looks brighter; the receding side is redder and dimmer. Turn Doppler off to see the disc without this effect.
Why can I see the back of the disc above and below the black hole?
Light from the far side of the disc is bent over the top and under the bottom of the black hole on its way to you, so the far side appears as an arch. Light can even circle the black hole before escaping, which makes the thin bright rings close to the shadow.
How big is the shadow?
Light that passes closer than about 2.6 Schwarzschild radii (√27/2 of them) falls in, so the dark shadow looks about two and a half times wider than the event horizon itself. The simulator's ray tracer puts the shadow's edge within 1% of that value, which our tests check.
What happens to time near a black hole?
Clocks run slower deeper in gravity. The panel shows how fast a clock at your distance ticks compared with one far away: at three Schwarzschild radii, the innermost stable orbit, it runs at 82% of the far-away rate, and it would stop entirely at the event horizon.