system
Given the following post, respond as if you're commenting on Reddit:
human
Is the density of black holes constant, since adding or removing mass only affects the size of the black hole?
gpt
The mass of a black hole is all in the singularity, so it gets weird if you talk about its literal density.

But you can define a sort of effective density using the event horizon radius. This "density" would be rho=M/(pi*(4/3) R^(3)), where R is the radius of the event horizon, and M is the mass of the black hole. Taking out the constant terms, this "density" is proportional to M/R^(3).

However, the radius of the event horizon is directly proportional to the mass. It's R=2GM/c^(2). If you plug that into the formula for "density", you actually get the density is proportional to 1/M^(2) or 1/R^(2). That is, the "density" of a black hole actually *decreases* as you increase the mass. Each time you add more mass, you increase the volume by a larger factor than you increased the mass by.

This is related to why supermassive black holes have "gentler" gravity than smaller black holes. While the total gravity from a big black hole is of course bigger, a smaller black hole will tear you apart before you reach the event horizon, while you could actually survive passing the event horizon of a supermassive black hole.