Black holes
Work out for yourself why a small enough ball of mass traps its own light, learn what an event horizon is and is not, and see the four independent ways we know black holes are really there.
THE IDEA
How fast do you have to throw something?
Throw a ball up and it comes back. Throw it faster and it goes higher. Throw it at 11.2 km per second and it never returns: that is the Earth's escape velocity. The number depends on two things only, the mass you are escaping and how far you are from its centre. The Moon needs 2.4 km/s. The Sun's surface needs 618 km/s. Now keep the mass the same and shrink the ball. You are getting closer to the centre, so the escape velocity climbs.
Squeeze hard enough and the required speed passes 300,000 km/s, the speed of light. Nothing can go that fast, so nothing can leave. That is a black hole: not new physics added on, but the old rule from lesson 03 followed to its end.
how small must a mass be squeezed to trap its own light?
the answer is simple: about 3 km for every Sun of mass.
the Earth -> about 9 millimetres
the Sun -> about 3 km
a 10-Sun star -> about 30 km
our galaxy's centre, 4 million Suns -> about 12 million kmthe last one is a ball wider than 17 Suns side by side, and it still fits comfortably inside Mercury's orbitNothing forces a mass to shrink this far. The Earth will never be 9 mm across. But when a core of more than about 2.5 Suns collapses, nothing we know of can stop it, and this is the size it passes.
Check yourself
Hooman asks why the Sun is not a black hole, since it is extremely massive. What is the right reply?
- Its fusion produces an anti-gravity effect
- Black holes only form from clouds of gas collapsing directly, never from a star like the Sun
- Escape velocity depends on distance too, and the Sun's surface is 700,000 km out
- The Sun is not heavy enough for gravity to matter
Show the answer
Escape velocity depends on distance too, and the Sun's surface is 700,000 km out
Right. Mass alone does not make a black hole; mass packed into a small radius does. To trap its own light the Sun would have to be squeezed from 700,000 km down to about 3 km.
Event horizon
The boundary around a black hole where the escape velocity reaches the speed of light. Inside it, every possible path leads inward. It is not a wall or a surface made of anything; it is a line drawn by what can still get out. Nothing marks it, and for a large black hole you could cross it without noticing.
The black hole people talk about is mostly this boundary, because that is all anyone can ever observe from outside. What is at the very centre, general relativity describes as a point of infinite density, which most physicists read as a sign the theory is incomplete rather than a real description.
Check yourself
If the Sun collapsed into a black hole tonight without losing any mass, the Earth would carry on in exactly the same orbit.
Show the answer
True
True, and it is the clearest test of what a black hole is. An orbit is set by the mass you go round and your distance from it, and neither of those would change: the same 150 million km, the same year. The sky would go dark after about 8 minutes, which is the real problem, but nothing would pull us in.
How we know: four independent lines of evidence
- Watch what orbits nothing
For decades telescopes tracked individual stars near the centre of our galaxy. One of them completes an orbit in about 16 years, whipping around an unseen point. The orbit gives the mass inside: roughly 4 million Suns, in a region smaller than our solar system. No cluster of stars could hide there.
- Watch the gas queue up
Matter falling toward a black hole does not drop straight in. It spirals into a flat accretion disk, and friction heats the inner part to millions of degrees, so it blazes in X-rays. The X-rays come from just outside the horizon, not from the hole itself.
- Listen for a collision
In 2015 detectors in the United States measured a ripple in spacetime lasting a fraction of a second. Its shape matched two black holes of about 30 solar masses each spiralling together and merging. Dozens more have been recorded since.
- Take a picture of the shadow
In 2019 a network of radio telescopes spread across the Earth published an image of the giant black hole in the galaxy M87: a bright ring of hot gas around a dark centre. In 2022 the same network imaged the one at the centre of our own galaxy.
Check yourself
Match each observation to what it actually shows
Show the answer
- A star looping around an empty point every 16 years → Millions of solar masses in a tiny volume
- X-rays from a very small region → Gas heated by friction just outside the horizon
- A ripple in spacetime lasting a fraction of a second → Two black holes merging into one
- A bright ring around a dark patch → Light from hot gas bent around the hole
UP CLOSE
Small ones are more dangerous than big ones
What tears you apart near a black hole is not the pull itself but the difference in pull between your head and your feet. Near a 10-solar-mass hole the horizon is only 30 km away from the centre, so that difference is enormous: you would be stretched into a thread long before you arrived. Near a 4-million-solar-mass hole the horizon is 12 million km out, the difference across your body is mild, and you would cross it alive and notice nothing at the moment of crossing.
Nothing good follows. Once inside, every path leads to the centre, and the trip is short. But the popular image of being shredded at the horizon is only true for the small ones.
Check yourself
- System A: a visible blue star circles an unseen companion every 5 days. The unseen object weighs about 15 Suns, and X-rays pour out of the region between them.
- System B: a visible star circles an unseen companion every 5 days. The unseen object weighs about 0.8 Suns and gives off no X-rays.
Which system holds a black hole, and what is the deciding number?
- B, because lighter objects collapse more easily
- A, because the unseen object is far heavier than any white dwarf or neutron star can be
- Both, since anything unseen is a black hole
- Neither; an unseen companion is always a dim star
Show the answer
A, because the unseen object is far heavier than any white dwarf or neutron star can be
Right. The orbit gives you the mass, and mass decides. A white dwarf stops at about 1.4 Suns and a neutron star at roughly 2 to 2.5. Fifteen solar masses in something that emits no light leaves one known option, and the X-rays from infalling gas fit it.
What to keep, and what is still open
- Keep: a black hole is mass squeezed inside the radius where escape velocity reaches light speed. About 3 km per solar mass.
- Keep: from a distance it pulls exactly like any other mass. The danger is that you can get close, not that it reaches out.
- Keep: we detect them by orbits, by X-rays from infalling gas, by gravitational waves, and now by imaging the shadow.
- Open: what happens at the centre. Infinite density is a sign that general relativity has run out of road there, and joining it to quantum physics is unfinished work.
- Open: Stephen Hawking argued black holes should slowly evaporate. For any real black hole the effect is far too faint to have been observed, so it remains a prediction.
Check yourself
Nastaran hears that our galaxy has a black hole of 4 million solar masses at its centre, and asks whether the Earth is slowly being pulled into it. What should you tell her?
- Yes, and we will reach it in a few billion years
- No. It is 26,000 light-years away, and we orbit the galaxy's whole mass
- Yes, but only when the Sun dies and releases us
- No, because the galaxy's rotation cancels out its gravity, the way a spin cancels weight
Show the answer
No. It is 26,000 light-years away, and we orbit the galaxy's whole mass
Right. At that distance those 4 million solar masses are a small part of what the Sun feels; most of the pull comes from the billions of stars and the dark matter spread through the galaxy. We circle the galactic centre once every 200 million years or so, the same way the Earth circles the Sun.
Lesson recap
- Escape velocity rises as you squeeze a mass smaller. Past about 3 km per solar mass, it exceeds the speed of light and nothing can leave.
- The event horizon is that boundary, not a physical surface. Everything we observe comes from outside it.
- A black hole's gravity at a distance is the same as any equal mass. It does not suck; it simply lets you get very close.
- Four independent methods find them: stellar orbits, X-rays from accretion disks, gravitational waves from mergers, and direct images of the shadow.
- Small black holes shred you before the horizon; huge ones let you cross unharmed. What lies at the centre is an open problem in physics.