[improbable22]

For black holes these aren't separate concepts. An apple and the earth each have rest mass, and gravity means there is also potential energy in their separation. But a black hole is an object with rest mass which is made purely out of gravity.

With two well-separated black holes it's reasonable to talk about each of their rest masses, and the potential, just like the apple. But as they get close and merge these ideas are hard to pin down, and stop being useful. Their shapes get blended together, and their horizons unite into one sphere, and for a while this wobbles around a lot before settling down. Some of the energy of its wobbling around departs as gravitational waves. Once it's settled down you can meaningfully talk about its rest mass again.

[mirimir]

OK, but what about the event horizon issue? So some stuff (GM) can escape the event horizon, but other stuff (matter, light) can't escape. So they must somewhat be separate concepts, because the event horizon affects them differently.

[improbable22]

No, not really. Just about everything we say about black holes is talking only about the exterior, the region of spacetime outside the horizon. The simulations through which we model the merging of two black holes only model the exterior of both. The curvature of this exterior is what gets all churned up during the collision, and some of it ends up travelling off as gravitational waves.

The fact that we can get away with studying only the exterior is really the same fact that the horizon is a horizon. The causality only goes one way, for everything not just for normal matter. And thus ignorance of the interior is no barrier to understanding the exterior.

[mirimir]

The article says basically: 7M BH + 12M BH -> 18M BH + 1M GW. But I'm getting the impression that this is misleading. Wouldn't it be more accurate to just say that the system had 19M before merger and 18M afterward?