Comment by pdonis
10 hours ago
> the mass density inside the event horizon
Is not a well-defined number. The number you are calculating assumes that the horizon is an ordinary 2-sphere enclosing an ordinary 3-ball [edited, see grandchild post] in Euclidean space, and divides the hole's mass by the calculated volume of that 3-ball. But the spacetime of a black hole doesn't work that way. The "space" inside the hole's horizon is not like any kind of ordinary space that your intuitions will work for.
Also, the interior of the hole is vacuum, so its mass is not something that's distributed throughout any kind of volume; it's just a geometric property of the spacetime.
You can't build an ordinary 3-sphere in 3D Euclidean space; a 3-sphere is a hypersphere. Are you considering 4D spacetime as the container of the 3-sphere, or did you just mean the volume of the 2-sphere in 3-space (as opposed to its shell area)?
Sorry, I meant to say 3-ball bounded by a 2-sphere in Euclidean space. The edit window of my GP post is still open so I've fixed it.