[micw]

What exactly is the "density" of a black hole?

As I understand, a BH is a singularity, so all mass is at one point which means all BHs have the same (infinite) density.

Is it a kind of "virtual density", e.g. the mass of the singularity devided by the schwarzschild radius or the event horizon?

[codethief]

I suppose OP defines it as the mass of the BH, divided by the apparent volume taken up by the BH (more precisely: the apparent horizon), as seen from the outside. Put differently, for a Schwarzschild BH: Density ~ M/R³ (modulo constant prefactors) ~ 1/M², since the Schwarzschild radius is linear in M.

[zycon]

Density is mass divided by volume. Volume of BH is defined by event horizon.

Singularity is a result of applying a theory of relativity in a case where we know relativity doesn't work, so it's unlikely it's real.

[codethief]

> Volume of BH is defined by event horizon.

The event horizon is a three-dimensional null hypersurface, though, encompassing a four-dimensional spacetime "volume". You are probably referring to the two-dimensional apparent horizon, which depends on the spatial slicing.