How is a Black Hole Created?
Outer space is host to all sorts of interesting objects. We have planets, stars, asteroids, and nebulae, but none of them are quite as fascinating or mysterious as black holes. The idea of a black hole was first proposed in 1783 by an English parson named John Michell and was later predicted by Karl Schwarzschild in 1916 using Albert Einstein’s theory of general relativity. Since then, we’ve made remarkable progress toward understanding how black holes work, helping us better make sense of the relationships between space and time. However, it wasn’t until 2017 that we got the first bit of photo evidence of a black hole, which bluntly depicted the bending of light around the event horizon.
As you can tell, we’ve made considerable progress toward better understanding these interstellar objects, and it was reading about black holes which had kickstarted my interest in astronomy and space over a decade ago. So, it’s not too surprising that once I found out that black holes were created by shrinking a normal-sized thing into a super-tiny-sized thing, it became my mission for about 5 solid minutes to make my own black hole. Turns out, it’s not that simple. And thankfully, my project wasn’t much of a success back then, but I’ve learnt a little more about how black holes are created since then.
So, just in case the gas prices here go over $2/L and it’s cheaper to delete the world than it is to drive to get groceries, let’s work through a case study of what it might take to turn the Earth into a black hole.
How is a black hole created?
There are 2 main ways this can happen, which seem to be quite polar. They can form by A) accumulating an incredible amount of mass in a given amount of space, or B) shrinking a given mass down to a minuscule amount of space. It’s important to note that either process ultimately involves density, as we are measuring the relation between the volume (simplified into the radius of a sphere) and the mass of an object. When we talk about shrinking down a mass, we mean increasing the density of the object by keeping the mass constant while decreasing its volume.
Both of the avenues to black hole formation depend on something called the Schwarzschild radius of an object, defined by the formula below where R is the Schwarzschild radius, M is the mass of an object, G is the universal gravity constant and c is the speed of light.
The Schwarzschild radius describes the event horizon of a black hole, which marks the outer edge from which nothing, not even light, can escape the immense gravitational pull of the black hole. Importantly though, if an object shrinks down to about or beyond its Schwarzschild radius, constantly increasing in density, it will collapse into a black hole.
Another important feature of the formula for the Schwarzschild radius is that G and c represent constant values—the universal gravity constant and the speed of light do not change between any calculations. The only variable remaining which affects the Schwarzschild radius is M, or the mass of the object. Thus, the Schwarzschild radius depends only on mass and is directly proportional such that an increase by factor x in an object’s mass would correlate to an increase by an equivalent factor x to its Schwarzschild radius. So, a more massive object has a larger Schwarzschild radius and therefore it may collapse into a black hole at a larger volume.
How small does the Earth have to get?
In our quest to turn the Earth into a black hole, our previous findings make it clear the only information we need in order to find the Earth’s Schwarzschild radius is the Earth’s mass, which is about 5.9722 × 10²⁴ kg. If you’re wondering how we got that number, the mass of planets can be predicted using the gravitational impact of celestial bodies; that’s complicated stuff we’re not going to get into, but if you’re interested, you can check out a quick summary here!
Let’s plug the Earth’s mass into our formula to get our planet’s Schwarzschild radius.
R = (2GM)/c²
R = (2 × [6.6743 × 10−11 m³ kg^-1 s^-2] × [5.9722 × 1²⁴ kg]) / (299792458 m/s)²
R ≈ 0.88 cm
0.88 cm. That’s it.
That’s a diameter of about 1.76 cm, which is smaller than a US penny at about 1.79 cm across.
So, if we wanted to turn the Earth into a black hole, we would have to shrink the planet down to a size smaller than the length of a dime, all while maintaining its original mass. Good luck.
I think it goes without saying that no human is capable of that, regardless of what you might bench. Unfortunately, that means that either you’ll have to walk to go buy groceries or look away while you buy gas. Or maybe take public transit to help out the environment. Yet, the big concern here isn’t that creating a black hole seems impossible for humans to do, but it seems unbelievable that a black hole can be created this way at all. It’s not like there’s a way around the math, the formula remains the same for all celestial objects and thus all calculations would follow the same scale as the one we just carried out for the Earth. So then, how do black holes form?
Natural black hole formation
Black holes are a product of the death of a massive star, typically multiple times as massive as our sun. So, to understand how stars die, we must first understand how they function to stay “alive”.
Crucially, stars aren’t rocky like the Earth, they’re masses of densely packed gases which by themselves don’t hold any definite form. The large gravitational forces of stars are not limited to planets and asteroids, but also act on the star itself, which is what gives them their characteristic spherical shape while simultaneously wanting to condense those gas particles into the smallest volume thermodynamically favourable. However, if the latter were to happen, we wouldn’t be able to see many stars at all—so there must be a contradictory force responsible for expanding the gases in a star, ultimately resisting the pull of gravity.
And indeed, there is such a process.
Nuclear fusion acts as the stellar power source. At the core of stars, with incredibly high pressures, temperatures, and energy, atoms fuse together to form new atoms and release energy in the process. Oversimplifying, hydrogen fuses with hydrogen to form helium and excess energy, helium then fuses with other helium atoms to form the next elements on the periodic table, which then follow suit to continue to merge nuclei and produce new, heavier elements as well as a constant outburst of energy. This consistent energy output propels gases outwards, and thus, a star can expand against the forces of gravity.
Great, so we have gravity which pulls the star’s matter inwards and nuclear fusion which pushes the star outwards. What goes wrong to make a star die?
Well, it turns out nuclear fusion doesn’t continue indefinitely. In massive stars that can progress through numerous stages of nuclear fusion, atoms will eventually fuse to form iron. However, iron just so happens to be the most nuclearly stable element in the universe and cannot undergo fusion simply because it would require a larger input of energy to fuse with another atom than it would release as a product. Thermodynamics strikes again. So, once there is a build-up of iron in a star’s core, nuclear fusion will drop even just momentarily. But at that moment, gravity (which acts as quickly as light itself) completely takes over the force balance of the star and causes it to condense and condense until its entire mass collapses in on itself, thus becoming a black hole.
Now, this might seem familiar. As gravity takes over, the mass of the star doesn’t change, but the volume it occupies in space decreases until the star is small enough to approach its Schwarzschild radius and become a black hole.
However, not all star deaths result in black holes. Smaller, less massive stars have a more stable decay, becoming dwarfs in a process that takes billions of years—much like what will happen to our sun. Not all black holes are formed from the collapse of dying stars either. Two incredibly dense, yet small neutron stars colliding and joining mass could assemble a great enough mass in a small enough volume to surpass its Schwarzschild radius and form a black hole.
Mystery remains
After all that we’ve learnt about black holes, there is still one major observation that we cannot seem to explain, one baffling, yet terrifying origin. Picture the Milky Way, our home spiral galaxy. Now try and imagine the centre of the Milky Way. Do you see a star? Maybe a massive planet? Maybe a solar system, or maybe even nothing at all. The question astronomers and astrophysicists have been trying to answer since we’ve learnt the answer to the previous question is: why is there a supermassive black hole at the centre of most galaxies?
It’s weird to think the Milky Way spirals around an enourmous black hole with a radius of 12 million km. Perhaps it’s scary but perhaps its poetic that everything we know orbits the closest thing we have to pure nothingness. My guess is as good as yours, so perhaps that’s a topic for another day.
