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We know that black hole mergers are a thing, as LIGO has detected gravity waves from these exact events.
To get too much more specific, we need to ponder the mass of the black holes and their distance of separation.
You did specify that these black holes were of equal size. They would orbit each other, potentially for billions of years, just like any two other massive objects and how these orbits behaved would depend on their mass, orbital distance, relative velocity and the gravitational influence of any other large bodies. For example, two 30 solar mass black holes orbiting close to Sagittarius A* (our galaxy's central super massive black hole) would have a very different orbital pattern from the same two black holes orbiting each other in intergalactic space.
Nitpick: Gravity wave ≠ gravitational wave :)
https://www.skyatnightmagazine.com/space-science/final-parsec-problem
So.. I was thinking about this. He's a weird thing..
When black holes merge don't the gravitational waves give us information about the motion of the singularities. It would seem natural that the point between black hole event horizons touching and the singularities finally merging generates huge gravitational disruption (and is very brief)
But isn't this a signal communicating something from within an event horizon?
I know what we detect now is extremely low resolution but it's the principal of the thing..
Well the gravitational waves come from a mass that is moving. It's like electromagnetic waves are created by a moving charge. But because gravity is so weak you need it to be a very big mass moving very fast to be detectable. When black holes merge they spiral in and at the last moment they get to extremely high RPM with all that mass moving very fast.
Kind of an interesting thought but I don't know if it really counts to say that the mass and location of the black hole is really "information from inside the horizon" even though technically the center of mass is inside the horizon.
Although we're solidly in the realm of fantasy thought experiment, it struck me that - in principal - if one was inside the black hole, with sufficient mass under your control, you could pass a signal to outside the hole by shifting the mass this way or that.
Obviously we're taking vanishingly small windows of time. But in principal it seems that you could react to something inside the horizon, exert your will on the movement of something super massive, and that be detectable to someone outside the horizon?
Wouldn't shifting the mass require pushing against another mass? In that case, might those two signals cancel each other out?