Which is caused by matter achieving a particular density. What we observe is not the matter but the _effects_ of the curvature created by that matter but to say they're not "made of matter" seems overly reductive here.
> some of the spacetime curvature doesn't get included in the merged hole
The observable mechanics of a black hole are (probably) controlled by it's surface area and not it's volume. When two spherical objects merge the surface area is less than the sum of the two original objects.
> Which is caused by matter achieving a particular density.
More precisely, by an isolated blob of collapsing matter surrounded by vacuum achieving a particular density.
> to say they're not "made of matter" seems overly reductive here.
No, it isn't, it is making a very important point: that the matter that originally formed the hole is not there any more. The hole itself is vacuum. If you fall into it, you won't see any matter, even though the hole was originally formed by collapsing matter.
> The observable mechanics of a black hole are (probably) controlled by it's surface area and not it's volume.
Only in the sense that the horizon area is proportional to the square of the mass, whereas the volume is not even well-defined. The actual thing that is controlling the "observable mechanics" is the mass (and spin, and charge if present, but in any actual hole it probably won't be).
Which is caused by matter achieving a particular density. What we observe is not the matter but the _effects_ of the curvature created by that matter but to say they're not "made of matter" seems overly reductive here.
> some of the spacetime curvature doesn't get included in the merged hole
The observable mechanics of a black hole are (probably) controlled by it's surface area and not it's volume. When two spherical objects merge the surface area is less than the sum of the two original objects.