Isn't our universe less dense than a black hole? |

Black Holes can be less dense than water, it's a pretty cool fact which can be seen with an easy calculation.

Density is mass divided by volume, so (p is density, M is mass, V is volume)

p = M/V

A black hole is a sphere which has volume V = (4/3)*(pi)*(R^3), with R the radius. Substituting for V in the first equation we have:

p = 3M/(4pi*R^3)

The radius of a black hole is its Schwarschild radius, which is:

R = (2GM)/(c^2)

G is Newton's constant and c is the speed of light. So replacing R in our formula for p with this, we get:

p = (3M*c^6)/(32pi*G^3*M^3)

Canceling the M factors and separating out the M factors:

p = ((3c^6)/(32pi*G^3))*(1/M^2)

The numbers in front are just some number which doesn't depend on the properties of the black hole (it's just multiples of the speed of light and G and pi), which I'll call C (= 7.6 x 10^79), so

p = C/M^2

So the density of a black hole is proportional to the inverse square of its mass. So the bigger the mass, the less dense the black hole. Make the mass big enough and the black hole can be less dense than water.