# The density of black holes

Black holes are the most extremely compact objects of the Universe. In fact, at their center lies a singularity: a point with zero volume, where all the mass of the black hole is compressed. The singularity is a region of infinite densitysomething that is not really conceivable by the human mind.

Something we can instead ask ourselves is: “What is the average density inside the Event Horizon of a black hole?” And we might enjoy the answers that Nature gives us quite a lot.

Density is a measure of how much mass is enclosed in a volume. The larger the mass in a given volume, the denser the object is. The smaller the volume of a given mass, the denser the object is.

For example, we can think to the density of citizens as a measure of the number of people in a city. Here the number of people represents the mass, while the size of the city represents the volume. If we add more and more people in a given city, the density of citizens will increase. Also, if we fix the number of people and we make the city smaller and smaller, the density of citizens will increase. Generally speaking then, a larger number of people and/or a smaller city gives a higher density of citizens (it would then be very easy for citizens to stumble upon each other!); while a smaller number of people and/or a larger city, gives a smaller density of citizens (you could easily walk around without seeing any other citizen for a while).

Now, (one of)the funny thing about black holes is: the size of their Event Horizon is proportional to their mass. In other words: the more massive is a black hole, the larger it is. In particular, if we double the mass of a black hole, we get a black hole volume eight times larger; if we increase the mass by a factor of three, the volume will get 27 times larger; and if we increase the mass of the black hole by a factor of ten, its volume will increase by a factor of 1000.

Think about it. If you double the number of people in your black hole city, the black hole city automatically becomes eight times larger. If you triple the number of people in your black hole city, the black hole city becomes automatically almost thirty times larger. If for any person of your black hole city you add 9 more people, your black hole city will become 1000 times bigger. What does this mean? The more people you add to the black hole city, the smaller density of citizens you get! For a black hole in the Universe: the larger its mass, the lower its average density will be.

#### Massive black holes are less dense than small mass black holes.

A black hole with the mass of a star like our Sun is extremely dense: about 1,000,000,000,000,000 times denser than the densest material on Earth.

A black hole of a thousand times the mass of our Sun is “only” 1,000,000,000 times denser than the densest material on Earth, while a supermassive black hole with a million times the mass of our Sun is just 1,000 times denser than the densest material on Earth.

#### But a black hole of a hundred millions times the mass of our Sun, is as dense as… water.

The largest black holes that we know have masses of about ten thousand millions times the mass of our Sun: they are in fact, on average, less dense than the Earth’s atmosphere.
The largest black holes we know would not only float in water, but they would also float in the air that humans breathe.

Our Universe is amazing, isn’t it?