[improbable22]

My first point about mass was that some are tempted to imagine the mass of the BH as residing in the matter of the neutron star or whatever that formed it. This is misleading, it is better to think of that matter as no longer existing, and just deal with the fact that pure Schwarzschild looks identical to a lump of matter, from a distance.

How you measure the mass, well my orbit example is admittedly crude, ADM mass is I think the right asymptotic concept.

By purely gravitational object I mean this: everything we're discussing here about merging and waves and accretion disks all concerns only the exterior. This is all vacuum Einstein, pure gravity. (Whether we can say anything sensible about the interior is another whole different rabbit-hole.)