# I’ll Drink to That

In Physics by Brian Koberlein4 Comments

For any black hole, there is a critical distance known as the Schwarzschild radius.  Get closer than the Schwarzschild radius, and the black hole has you.  You become trapped like a fly in amber and can never escape.  The Schwarzschild radius defines a spherical surface known as the event horizon.  The region of no return is therefore the volume enclosed by the event horizon.

You could say the volume enclosed by the event horizon is the volume of the black hole.  Since its is a sphere, then its volume is proportional to the cube of the  Schwarzschild radius.  But the size of black hole is proportional to its mass.  This means the radius increases linearly with mass.

Here’s where it gets fun.  Given the mass and volume of a black hole, you can define its average density.  Simply take its mass and divide by its volume.  Since the radius increases linearly with mass, but volume increases as the radius cubed, this means that the average density of a black hole goes down as its mass gets bigger.  There are supermassive black holes in the center of some galaxies that have masses a billion times larger than our sun, which means their average densities can be less than that of water.

So the next time you have a cold drink, just remember that you are drinking something that has a greater average density than the largest known black holes.  How awesome is that!

## Comments

1. Very well but there is a little mistake:It is exactly what happens in the sun, in the stars and in all other space bodies, including planets, the density is higher at the center than in the suburbs,

1. Author

That’s the point. Calculating averages can be misleading.

2. What would the mass of a black hole have to be to have the density per cubic meter equal to the CMBR

3. 4 x 10^19 solar masses = 8 x 10^49 kg. Mass density = 10^-20 kg/m^3. Temperature = 2977 K.