Chapter 6 · From a collapsing star to a ripple in space-time
Black holes
The point of no return
Imagine throwing a ball upward. It falls back unless you throw it at the escape velocity, which is 11.2 km/s for the Earth. The heavier and smaller an object is, the higher that speed. When a massive star runs out of fuel, its core can collapse so far that the escape velocity passes the speed of light, 299,792 km/s. The boundary where this happens is the event horizon. Inside it nothing can come back out, not even light. Stars of more than roughly 20 times the mass of the Sun are thought to end like this. The idea of a dark star was first discussed by John Michell in 1783.
How small is a black hole?
In 1916, a few months after Einstein published general relativity, Karl Schwarzschild found the size of the horizon: r = 2GM divided by c squared, where G is the gravitational constant, M the mass and c the speed of light. Worked example for the Sun: its mass gives r of about 2.95 kilometres, so the Sun squeezed into a ball with a radius of 3 km would be a black hole. For the Earth the radius is about 9 millimetres, the size of a pea. In the sandbox move the mass and see the radius. The Milky Way's central black hole, Sgr A*, has about 4 million solar masses and a radius of roughly 12 million km.
Spaghettification
A black hole does not suck. If the Sun were replaced by a black hole of the same mass, the Earth would keep orbiting just as it does now. The danger is only in getting close. Gravity gets stronger as you approach, and the pull on your feet is stronger than on your head. This difference, called a tidal force, stretches an astronaut into a long thin shape, which scientists call spaghettification. For a small black hole it happens before the horizon, while for a giant one it happens inside it. Gravity also slows time: a clock near the horizon ticks slower, as seen from far away. A weaker version of the same effect is corrected in the clocks of GPS satellites.
The shadow of M87*
A black hole is dark, but the gas around it glows. On 10 April 2019 the Event Horizon Telescope, a network of radio dishes on several continents that acts like a telescope as big as the Earth, showed the first image of a black hole: a bright ring around a dark shadow in the galaxy M87, about 55 million light-years away. The black hole has a mass of about 6.5 billion Suns, and its horizon is roughly 130 times the distance from the Earth to the Sun, wider than our whole planetary system. The ring is lopsided because the gas on one side moves towards us.
Our own black hole
On 12 May 2022 the same team presented the black hole at the centre of our Galaxy, Sagittarius A*, about 27,000 light-years from us. It is far smaller, about 4 million solar masses, and the gas around it changes within minutes, which made the picture harder to make. It also shows a ring. The two images, of the biggest and our nearest giant, look alike, which supports Einstein's general relativity. The picture is not a photograph in the ordinary sense: it was assembled from radio signals recorded at different places and combined by computers.
Ripples from a collision
When two black holes circle each other and merge, they shake space itself, sending out gravitational waves. LIGO detected the first on 14 September 2015 and announced it on 11 February 2016. Two black holes of 36 and 29 Suns merged into one of 62, 1.3 billion light-years away. Worked example: 36 + 29 = 65, but 62 was left, so about 3 solar masses vanished and turned into gravitational waves through E = mc². LIGO measured a change in length thousands of times smaller than the width of a proton. The discovery received the Nobel Prize in Physics in 2017.
In numbers
- ≈ 3 km
- the Schwarzschild radius of the Sun
- 2019
- the first image of a black hole, M87*
- 14 Sept 2015
- LIGO detects the first gravitational waves