Question: What is the highest density you can reach without creating a black hole

Edward Banks answered on 19 Mar 2020:

Let’s do some maths on this! A black hole is defined by an event horizon, beyond which the escape velocity is greater than the speed of light.
For a given mass M, the size of the event horizon (also called the Schwarzchild radius) is given by 2*G*M/c squared; where G is Newton’s gravitational constant and c is the speed of light.
Now a black hole is a sphere, so it has a volume given by 4*pi*r cubed / 3.
Substituting in r from the Schwarzchild radius, this means the volume V = 32*pi* G cubed * M Cubed / 3 * c ^ 6
Density (P) is simply Mass M divided by Volume V, which is P = 3* M * c ^6 / 32 * pi * G cubed * M cubed
Which cancels down to P = 3 * c ^ 6 / 32 * pi * G^3 * M^2
We can calculate all the values except M here, which gives us P = 7.7 * 10^79 / M ^ 2

So the density is actually dependent on the inverse of the mass squared. The more mass you have, the lower density you need. So what is the highest density you can reach without creating a black hole? Depends on your mass.