They can merge event horizons on a finite timescale from the outside and still take an infinite amount of time to merge singularities or whatever it is that singularities do when they meet up in the privacy of an event horizon.

Subject to local laws and conventions, of course.

An observer falling into the black hole would not observe any distortion in time. They would simply fall in, under the influence of gravity. From the perspective of a far-away observer it would look as if time is slowing down as the photons would take increasingly longer to escape. At the event horizon the photons would effectively be held in place. Eventually though, the last photon will have escaped and you will just observe a slightly larger black hole.

So the merger definitely happens from the point of view of the black holes. We might observe odd artifacts but they would eventually fade away.

> From the perspective of a far-away observer it would look as if time is slowing down as the photons would take increasingly longer to escape.

Photons travel at the speed of light always, that's what Einstein told us.

So rather, the observed energy (frequency) of the photons decreases, and it takes longer between each photon.

At least that's my understanding.

Black holes' radius is linear in proportional to their mass, they are not constant density, larger ones are less dense. Therefore, when a 5 solar mass BH merges with another 5 solar mass, the radius doubles, surface area quadruples, and volume goes up 8x. If they "never actually merge", SMBHs would not exist.

Collision is when they approach each other, then round down to one black hole.