Black hole simulator

A black hole simulator shows what a black hole does to the light and time around it. Our Black Hole Simulator traces real light paths past a non-spinning black hole: rays far out bend a little, rays closer in wrap round it, and any ray aimed inside 2.6 Schwarzschild radii falls in. It draws the event horizon, the photon sphere and the shadow to scale, and compares a clock near the hole with a distant one.

It opens on a black hole of 10 solar masses with a beam of light coming in from the left. Every path is worked out from the Schwarzschild solution of Einstein's equations, not drawn by hand.

Try it

Black Hole Simulator

Watch light bend and time slow down near a black hole

Open the simulatorGo to its page

How to use the black hole simulator

1. Under Light, choose Parallel beam, a row of rays coming in from far away, or Point source, a lamp you can drag near the hole.
2. For a beam, move the Highlighted ray height slider to pick one ray, and read how far it is bent and how close it gets. Set how many Rays to draw, from 4 to 48, and how far out to view.
3. Under Black hole, set the Mass, from 1 to 10 billion Suns. The sizes in km scale with it; the shapes of the paths do not.
4. Drag the near clock towards the horizon. Press play under Run and watch it fall behind the far clock.
5. Read the panel: the Schwarzschild radius, the photon sphere and the shadow radius in km, the highlighted ray's bending, the clock rate, the rate in an orbit there, and the redshift.

Distances on the stage are in Schwarzschild radii, Rs. A small inset shows the black hole as seen from far away, with its shadow 2.6 times the size of the horizon. Practice and help sets questions on the Schwarzschild radius, clocks, the photon sphere and light bending, with worked solutions.

The sizes that matter: horizon, photon sphere and shadow

The Schwarzschild radius comes from the mass:

Example 1: the Schwarzschild radius

For one solar mass, M = 1.989 × 10³⁰ kg:

Rs is proportional to the mass, so the simulator's 10 solar mass hole has Rs = 29.5 km, a photon sphere at 44.3 km and a shadow radius of 76.7 km. Set the mass to 4 million Suns, about the mass of Sagittarius A* at the centre of our galaxy, and Rs becomes 1.18 × 10⁷ km. Try one in the course, then press Mark:

Light bending and gravitational lensing

A ray that passes the hole at a distance b, called the impact parameter, is bent towards it. The closer it passes, the more it bends. The simulator works out each ray's bending exactly:

Far from the hole, the bending matches Einstein's weak-field formula, α = 4GM/(c²b) = 2Rs/b in radians. Close in, the real bending grows much faster, and at 3√3/2 = 2.598 Rs it becomes endless: a ray there circles the photon sphere. At 2.6 Rs the simulator gives 390°, more than a full turn. The opening setup highlights the ray at 2.8 Rs, which is bent by 132°. For light grazing the Sun, the same formula gives 1.75 arcseconds, the bending Einstein predicted and the 1919 eclipse measurements tested.

This bending is gravitational lensing. A black hole in front of a distant star bends the star's light round both sides, so the star can appear as two images or a ring. Use Point source and drag the lamp to see light from one place spread round the hole.

Time near a black hole

A clock held still at a distance r from the hole runs slow compared with a clock far away:

Example 2: a clock at 2 Rs

At r = 2 Rs the rate is √(1 − ½) = 0.707. While 60 s pass on the far clock, the near clock ticks 60 × 0.707 = 42.4 s. Drag the near clock to 2 Rs and the simulator gives a clock rate of 0.707, a rate of 0.500 for a clock orbiting there, and a redshift of z = 0.414: light from the clock arrives stretched to 1.414 times its wavelength. At the opening position, 3.11 Rs, the rate is 0.824.

At the horizon the rate falls to zero: a distant observer never sees anything cross it. Inside the photon sphere, no orbit exists, which the simulator shows as "No orbit".

What the simulator does not show

• A side view, not a picture. It draws light paths in a flat slice through the hole, plus a small inset of the shadow. It does not render a glowing disk of gas like the films do. For a 3D view, the Black Holes course has an interactive anatomy of a black hole.
• Non-spinning black holes only. It uses the Schwarzschild solution. Real black holes spin, which the Kerr solution describes, and that shifts the photon orbits.
• No falling in. It traces light and holds clocks still; it does not follow an object falling through the horizon, or spaghettification.

Common mistakes

• Thinking the shadow is the horizon. The shadow seen from far away is 2.6 times the horizon's radius, because light that comes close is bent in.
• Thinking a black hole sucks things in from far away. At a large distance its gravity is the same as any object of the same mass. Replace the Sun with a one solar mass black hole and the Earth's orbit would not change.
• Using the weak-field formula close in. 2Rs/b is only accurate far from the hole. At 3 Rs it gives 38°, against the true 98.5°.
• Mixing up the two clock rates. A hovering clock runs at √(1 − Rs/r). An orbiting one runs slower still, because its speed slows it too.

Learn more about black holes

The Black Holes course goes from escape speed and how massive stars die to the event horizon, lensing, time near a black hole and Hawking radiation. How stars end, as neutron stars or, for the most massive, black holes, comes up in High School Physics practice, and in GCSE Physics Higher in the UK. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. Our guide to the biggest black holes covers the record holders, and the Escape Velocity Calculator shows how fast you need to go to leave any planet or star.

Read next

Physics · SpaceWhat is the biggest black hole? Black holes explainedWhat a black hole is, what is inside one, what they look like, the biggest and closest known black holes, and whether one could ever hit Earth.