There's no "purely gravitational object" it only "looks like that" from behind the event horizon
We know the escape velocity > c and that's pretty much it, for GR it's a singularity (which usually means the theory is incomplete in that circumstance) and we don't know how QM work when squeezed harder than a Neutron star
> The mass of a black hole is something that's really only defined from a distance away.
If you mean "we can sense the gravitational field of something having mass X at a distance D larger than the event horizon" I agree.
But I'd rather say "we don't know what happens there" instead of "singularity" (which is what the current theories say it's inside and from the point of view of Relativity they're not wrong)
