How does water density compare to Black hole mean density inside The Scharwtzchild radius of mass 10^39k?

Answer 1

A black hole of mass M has Schwarzchild radius R=2GM/c^2. A sphere of this radius would have volume (4/3)piR^3=32pi G^3M^3/(3c^6). The density of water is 10^6 kg/m^3, so a sphere of that radius would have a mass of

32*10^6 pi G^3 M^3/(3c^6).

Let's divide this by M: if the answer is more than 1, the water sphere is more dense. If it is less than 1, then the black hole is.

So we want to evaluate
32*10^6 pi*G^3 M^2/(3c^6).

With M=10^39kg, G=6.67*10^(-11), and c=3*10^8 in SI units,
we get about 13000, so the sphere of water is about 13000 times as dense as a black hole that size would be.

Neat huh?

Answer 2

It is about 12 times as dense as Uranus.