Suppose we have two black holes moving on a path of direct frontal collision. Is it correct that from far away, due to time dilation, we can never "detect" that the two black holes merging or colliding? Would we perceive the relative motion of the two black holes slow down before the two event horizons touch? if that is the case:
question: Will a planet orbiting the system from far away feel a uniform distribution of mass located at the center or that of two blobs next to each other?
Is it correct that from far away, due to time dilation, we can never see the two black holes merging or colliding?
Correct. By definition you never see a horizon unless you cross it.
Would we perceive the relative motion of the two black holes slow down before the two event horizons touch?
Yes
will a planet orbiting the system from far away feel a uniform distribution of mass located at the center or that of two blobs next to each other?
It will feel more and more like that as time goes on. Of course, that isn't becsuse you feel mass that is far away. It is because the spacetime out near you evolves to be more an more like that. More and more like the kind of curvature that in the Newtonian weak field limit looks more and more like the effect of a large uniform distribution of mass.
It is confusing to me how you will perceive (based on electromagnetic radiation of increasing wavelength) that the two holes freeze before merging, and at the same time have a gravitational signature that looks like they fused
The gravitational signature never looks like they fused. In fact unless those black holes have been around forever we can still see the infalling material that made each of them. And in fact the infalling matter on the north side of one and the south side of the other one could decide at any moment to lose their courage and take off. And then the matter next to that could take off. And so on. The definition of the horizon is the events where they waited too long. We never see that by definition. So everything we see is events prior to that. So we see events prior to the too late.
So we always see matter where it isn't too late. So everything we see could come back out at us. Maybe it has to wait to get really symmetrically distributed before they can collectively push off and not leave things behind.Everything you see that looks similar to a black hole could still rip itself apart before it actually forms.
So it most definitely doesn't ever look fully fused. It just looks closer to merged. The electromagnetic appearance is a consequence of the time dilation, it doesn't cause it. In fact the black hole appears less massive over time as the light comes away from it.
Again, you can feel it from the curvature outside, you don't have to look electromagnetically. You could send neutral particles to orbit it in different planes and note the period to circumference and notice the ratio settles down in a way that doesn't depend on the plane you select.
Luckily black holes emit Hawking radiation, so in some sense we can see them.
So first there are two glowing balls approaching each other, after some time there will be one glowing ball that is twice as large as one of the initial glowing balls. (I'm considering black holes of same size)
And during the collision the balls distort to other shapes and shake violently emitting gravity waves.
All that happens quite fast when observed from far away. From closer observation point it happens even faster.
Just so that things don't become too absurd, all kinds of measuring instruments, like eyes and gravimeters, should agree what is happening during the merging.
