Gravity taken to its limit. Around the black disk of the event horizon — the point of no return, at the Schwarzschild radius Rs = 2GM/c² — a glowing accretion disk of gas spirals in at nearly light speed, one side beamed bright as it sweeps toward you and the other dimmed as it turns away. Encircling it all is the thin photon ring, where gravity bends light into orbit. Change the mass and read off the real sizes of the horizon, the photon sphere and the innermost stable orbit. It all runs on your device.
The bright side of the disk is beamed toward you — relativistic Doppler beaming
Presets
Mass10 M☉
Schwarzschild radius Rs—
Photon sphere (1.5 Rs)—
Innermost stable orbit (3 Rs)—
Accretion diskOn, orbiting from 3 Rs
Doppler beamingApproaching side brighter
Size ladder (log scale): the event horizon (Rs), photon sphere (1.5 Rs) and ISCO (3 Rs) plotted in km against fixed real-world sizes — Mt Everest, a large city, the Moon and the Earth. Move the mass and the three coloured markers slide along the scale while the grey landmarks stay put, so you can read straight off how far the horizon has grown past them.
One radius sets the scale of everything. A non-rotating black hole is defined by a single number, its mass, and from it comes the Schwarzschild radius Rs = 2GM/c² — the size of the event horizon, only about 3 km for the Sun's mass. The photon sphere where light can orbit sits at 1.5 Rs, and the innermost stable circular orbit that the accretion disk cannot cross lies at 3 Rs. The main view is illustrative — sizes and colours are not to scale, and there is no ray-traced gravitational lensing — but those three radii are the exact formulas, and the size ladder below plots them in km against real-world landmarks.
Reading the simulation
What the dark disk, the bright ring and the lopsided glow are telling you.
1
The event horizon — the point of no return
The solid black disk in the centre is the event horizon at the Schwarzschild radius Rs = 2GM/c². Nothing that crosses it escapes — not matter, not light — so it reads as a true shadow. Its radius grows in exact proportion to the mass: the readout and the size ladder both update from Rs = 2.953 km per solar mass as you move the slider or pick a preset, and you can watch the horizon marker slide past Mt Everest toward the Moon as the mass climbs.
2
The photon ring at 1.5 Rs
The thin bright circle just outside the shadow marks the photon sphere at 1.5 Rs, where gravity bends light sharply enough that photons can orbit. Light grazing this radius loops around and comes back to you as the sharp photon ring — the feature the Event Horizon Telescope imaged. On the size ladder it is the gold marker, sitting just to the right of the horizon at 1.5 times its distance.
3
Why the accretion disk looks lopsided
The glowing disk starts at the ISCO at 3 Rs — its inner edge — and orbits at a large fraction of light speed. The side sweeping toward you is beamed brighter (labelled on the left); the side turning away is dimmed. That is relativistic Doppler beaming, and it is why real black-hole disks look one-sided. Remember the picture is illustrative — the radii are exact, but the brightness, colours and lack of lensing are only suggestive.
How It Works
A horizon set by the mass, a ring of trapped light, and a disk that beams itself.
1
Mass sets one radius
A non-rotating black hole is described by its mass alone. Squeeze that mass into a small enough space and escape velocity reaches the speed of light at the Schwarzschild radius Rs = 2GM/c² — about 3 km for the Sun, 30 km for ten solar masses. Everything else scales from it: the photon sphere at 1.5 Rs and the ISCO at 3 Rs are fixed multiples, so a heavier black hole is simply a larger copy.
2
Light can orbit at the photon sphere
At 1.5 Rs gravity bends light so hard that a photon can circle the hole. Rays grazing this radius loop around and escape, forming the bright, thin photon ring around the dark shadow. Its size is a direct measure of how severely the black hole warps spacetime, and it is what makes the shadow appear slightly larger than the horizon itself in real images.
3
The disk heats, orbits and beams
Gas falling in cannot dive straight down; it settles into a disk and spirals inward, heating to millions of degrees and glowing — blue-white in the fast inner regions, cooling to orange further out. The inner edge is the innermost stable circular orbit at 3 Rs; inside it matter plunges in. Orbiting near light speed, the approaching side is Doppler-beamed brighter, giving the lopsided look.
What is a black hole?
A black hole is a region of space where gravity is so strong that nothing, not even light, can escape once it crosses the boundary called the event horizon. It forms when enough mass is squeezed into a small enough region — for example the collapsed core of a massive star. From outside you cannot see in; you can only see matter and light behaving in extreme ways around it, like the glowing disk in this visualisation.
What is the Schwarzschild radius and the event horizon?
The Schwarzschild radius Rs = 2GM/c² is the size of the event horizon of a non-rotating black hole of mass M — the distance from the centre at which escape would require the speed of light. Anything that crosses it is trapped. For the Sun's mass it is only about 3 km; it grows in proportion to the mass, so a ten-solar-mass black hole has a horizon about 30 km across. Change the mass here and the Schwarzschild radius updates from that exact formula.
What is the photon ring or photon sphere?
The photon sphere sits at 1.5 times the Schwarzschild radius, and it is the radius at which gravity bends light so sharply that photons can orbit the black hole. Light skimming past at that distance loops around, producing the bright, thin photon ring you see encircling the dark shadow of the hole in real images like the Event Horizon Telescope's. It is a direct fingerprint of how strongly the black hole curves spacetime.
Why is one side of an accretion disk brighter?
Matter spiralling into a black hole forms a hot, glowing accretion disk that orbits at a large fraction of the speed of light. The side of the disk sweeping toward us is brightened and blue-shifted, while the side moving away is dimmed and red-shifted — an effect called relativistic Doppler beaming. That is why real and simulated black-hole disks look lopsided, with one side far brighter than the other, as shown here.
A ready-to-assign lab using the simulation above. Free to use — nothing to install or sign up for, and no student data leaves the browser.
High school, College10–20 minInteractive simulation
Learning objectives
Describe how gravity bends the path of light.
Explain what the event horizon is.
Relate the Schwarzschild radius to mass.
Variables to change
Black hole mass
Light-ray impact parameter
Viewing angle
Procedure
Send light rays past the black hole at a large distance and observe their paths.
Move the rays closer and watch the bending increase.
Increase the mass and observe the event horizon and lensing grow.
Observations
Note how the bending of light changes with distance from the black hole and with its mass.
Questions
What is the event horizon?
What happens to light that passes close to a black hole?
How does the Schwarzschild radius depend on mass?
Does a black hole’s gravity differ from ordinary gravity far away?
Why do we see a dark shadow with a bright ring around a black hole?
Explanation
Massive bodies curve spacetime and bend light. A black hole is so dense that within its event horizon (r_s = 2GM/c²) escape is impossible. Passing light is lensed into arcs and rings, while its distant gravity behaves like any equal mass.
Answer key (for instructors)
1. The boundary around a black hole within which nothing, not even light, can escape.
2. Its path bends (gravitational lensing); very close in, it can be captured.
3. It is proportional to mass: r_s = 2GM/c². More massive black holes have larger horizons.
4. No — at a distance it pulls like any mass of the same amount; the extreme effects appear only close to the horizon.
5. Light near the horizon is bent and captured, leaving a dark region rimmed by lensed light.
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