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Black Holes: an interactive course

Published 8 Nov 20265 min read

Black Holes is an interactive black holes course that explains what black holes are, how they form and how we know they exist. Its 25 short sections cover escape speed, how massive stars die, the event horizon and its radius, the photon sphere, the singularity, types of black hole, gravitational lensing, time near a black hole, spaghettification, Hawking radiation, the first pictures of black holes and gravitational waves.

It opens with light rays fired past a black hole at a fan of angles, traced with the real equations: distant rays bend, closer ones swing round, and one loops the photon sphere.

What the course covers

Sections	Topic	What you do
1 to 3	What a black hole is, and escape speed	Work out a squeezed planet's new escape speed
4 to 5	How massive stars die	Order the stages of a star's life and death
6 to 10	The event horizon, the photon sphere and the singularity	Find a horizon radius from a mass, then decide whether a light ray escapes
11 to 12	Types of black holes	Classify black holes as stellar, intermediate or supermassive
13 to 16	Gravitational lensing and time near a black hole	Match lensed pictures, then work out how slow a clock runs
17 to 20	Spaghettification and Hawking radiation	Sort myths from facts, then rank black holes by temperature
21 to 25	Pictures of black holes, gravitational waves and the evidence	Sort the evidence, then what is known from what is still unknown

Escape speed and the event horizon

Escape speed is how fast you must go to leave a world for good: 11.2 km/s for the Earth. Squeeze the same mass into a smaller space and escape speed rises. When it reaches the speed of light, nothing can get out, and that boundary is the event horizon. Its radius, the Schwarzschild radius, is about 3 km for each Sun's worth of mass.

r_s=\frac{2GM}{c^2}The Schwarzschild radius, from section 6

The photon sphere sits at 1.5 times the horizon radius, where light can orbit the black hole

Strange effects

Mass bends light, so a black hole acts as a lens, turning a galaxy behind it into arcs or a ring. Gravity also slows time, so a clock near the horizon ticks slower than one far away. Tidal forces stretch anything falling in, which is spaghettification, and Hawking radiation means black holes slowly lose energy, the smallest fastest.

How we know

Black holes are seen through what they do: stars orbiting an unseen mass, glowing discs of hot gas, the first images of a black hole's shadow, and gravitational waves from black holes merging. The course ends by separating what is known from what is still unknown, such as what happens at the singularity.

Try a question from the course

Escape speed depends on the square root of mass divided by radius: v = √(2GM/r). Squeeze the Earth to a quarter of its radius and M/r becomes 4 times bigger, so escape speed goes up by √4 = 2 times, from 11.2 km/s to 22.4 km/s.

Now work out the escape speed for a new squeezed or heavier world, then press Mark to check your answer in the course.

Press Mark to have your answer marked in the Black Holes course.

Who this course is for

A-level and other advanced physics students meeting the Schwarzschild radius and astrophysics options.
Curious learners who want the real physics behind black hole headlines and films.
Younger students who love space and want to go further than a picture book, with the maths kept short.

What you need to know first

The course page lists Laws of Motion and Light & Energy. You will use square roots and standard form, and the formulas are explained as they come up.

How long it takes

There are 25 sections and most take a few minutes. Learners without a plan can open two sections of a course a day, in order, so the whole course takes 13 days. A plan removes the daily limit and lets you go straight to any topic, such as time near a black hole.

Guided courseThe Big Bang TheoryFrom black holes to the whole universe: expansion, redshift, the cosmic microwave background and dark energy.

Common questions

Is this black holes course free?

You can take every section without paying, two sections a day, in order. A plan removes the daily limit and opens any section straight away.

What is a black hole?

A region where gravity is so strong that nothing can escape, not even light. Its boundary is the event horizon.

How do black holes form?

Most form when a very massive star runs out of fuel. Its core collapses under its own gravity, and if the remaining mass is large enough, nothing can stop the collapse.

What is the event horizon?

The boundary around a black hole beyond which escape speed is faster than light, so nothing that crosses it can get back out. For a non-spinning black hole its radius is 2GM/c².

What would happen if you fell into a black hole?

For a small black hole, tidal forces would stretch you before you reached the horizon. For a supermassive one, you could cross the horizon without noticing anything at first, but you could never come back.

How do we know black holes exist?

From stars orbiting an invisible heavy object, from X-rays given off by hot gas falling in, from images of a black hole's shadow, and from gravitational waves detected when black holes merge.

Revision cards

Say the answer first, then flip the card to check it.

Where to go next

Solve it
Escape Velocity Calculator
Calculate escape velocity from a body
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Black Holes
The most mysterious objects in the universe, brought closer with science
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A-level Physics: Year 2
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