system
Given the following post, respond as if you're commenting on Reddit:
human
Why does a black hole gets less denser when you add mass to it? Shouldn't gravity make it even more dense?
gpt
We don't really know what happens when mass goes beyond the Swarzschild radius. Mathematically, at the center of a black hole is a singularity, which is a point with infinite density, but that seems to be unphysical. Since we don't know how matter is distributed in a black hole, we can't really make a definitive statement on its density.

Which is why the "density of a black hole" is typically defined as the ratio between the mass of the black hole and the volume enclosed by the Schwarzschild radius. This is a reasonable definition in the sense that a homogenous distribution of mass in this entire volume exerts the same gravitational force on objects outside the Schwarzschild radius as a distribution where the mass is more localized in the center or even the limit case where all mass is gathered in a single point.

Since the Schwarzschild radius is proportional to the mass and the volume is proportional to the cube of the Schwarzschild radius, that makes the volume proportional to the cube of the mass. And since density is mass over volume, that means that the density is proportional to the inverse of the square of the mass.