I take your point, but if at the heart of each BH is a singularity in which gravity is infinite, then even breaking out your calculator will not prevent collision.
You have been told the answer to this a number of times and still seem to repeat layman untruths.
The sort of singularity you describe
only appears directly in the static black hole situation.
The static solution is probably totally unnatural like finding a sun not rotating. Conceptually you can imagine such a thing and the mathematics will explode in your face as an indication of how unnatural and unstable the thing is you have described much less how you would ever create the situation.
As I said the simple laws that govern the ignition coil on your car says that it will produce infinite voltage ... you don't seem to have a problem with that?
How about if I ignore friction then a pushed ball rolls infinitely you don't seem to have a problem with that?
BE CONSISTENT you have a problem with projected infinities start with more down to earth ones.
The detected black holes were rotating (as expected) and merged to a rotating black hole (as expected).
There are only two known exact solutions to a rotating black hole being (a)Kerr and (b)Kerr–Newman descriptions. Most scientists prefer the Kerr metric because the Kerr-Newman has a characteristic we generally don't see by observation.
Perhaps Bill S rather than repeat layman junk and BS you do some reading on what the exact Einstein solutions of a rotating black hole predict. That is bother to actually check rather than parrot other layman.
In a Kerr metric you get metric infinities in a surface description. So "no point" like in the static solution its a surface and the infinity is no different than the projected voltage infinity of an ignition coil. It's simply a value that if you ignore all the actual other details it mathematically projects to it isn't real. One of the things we will now be able to determine is what local factors control the maximum value. For your car ignition coil that is characteristics of the wire and air in and around the coil.
