I feel the obvious answer should be "no" but help me think this through. It came from the previous Q on blackholes and am posting here for more visibility.
So considering two blackholes rotating about each other and eventually combining. It's in this situation that we get gravitational waves which we can detect (LIGO experiments). But what happens in the closing moments when the blackholes are within each others event horizon but not yet combined (and so still rotating rapidly about each other). Do the gravitational waves abruptly stop? Or are we privy to this "information" about what's going on inside an event horizon.
Thinking more generally, if the distribution of mass inside an event horizon can affect spacetime outside of the horizon then what happens in the following situation:
imagine a gigantic blackhole, one that allows a long time between passing the horizon and being crushed. You approach the horizon in a giant spacecraft and hover at a safe distance. You release a supermassive probe to descend past the horizon. The probe is supermassive in the way a mountain is supermassive. The intention is to be able to detect it's location via perturbation in the gravity field alone. Similar to how an actual mountain causes a pendulum to hang a miniscule yet measurable distance off the vertical.
Say the probe now descends down past the horizon, at some distance off the normal. Say a quarter mile to the 'left' if you consider the direction of the blackholes gravitational pull.
Let's say you had set the probes computer to perform some experiment, and a simple "yay/nay" indicated by it either staying on its current course down (yay) or it firing it's rockets laterally so that it approaches the direct line been you and the singularity and ends up about a quarter mile 'right' (to indicate nay).
The question is, is the relative position of the mass of this probe detectable by examining the resultant gravitational force exerted on your spaceship? Had it remained just off of centre minutely to the 'left' where it started to indicate the probe communicating 'yay' to you, or has it now deflected minutely to the right indicating 'nay'?
Whether the answer to this is yes or no, I'm confused what would happen in real life?
If the probes relative location is not detectable via gravity once it crosses the horizon, what happens as it approaches? Your very sensitive gravity equipment originally had a slight deviation to the left when both you and probe were outside the horizon. Does it abruptly disappear when it crosses the horizon? If so where does it go? The mass of the probe will eventually join with the mass of the singularity to make the blackhole slightly more massive. But does the gravitational pull of its mass instantly change from the location in the horizon where it crossed (about a quarter mile to the 'left') to now being at the singularity directly below. Anything "instant" doesn't seem right.
Or.. it's relative position within the horizon is detectable based on you examining the very slight deviations of your super sensitive pendulum equipment on board your space craft. And you're able to track it's relative position as it descends, until it's minute contribution to gravity has coalesced with the main blackhole.
But if this is the case then aren't we now getting information from within the horizon? Couldn't you set your probe to do experiments and then pass information back to you by it performing some rudimentary dance of manoeuvres? Which also seems crazy?
So both options seem crazy? Which is it?
(Note, this is a thought experiment. The probe is supermassive using some sort of future tech that's imaginable but far from possible by today's standards. Think a small planet with fusion powered engines or whatever. The point is, in principle, mass is detectable, and mass is moveable. Is this a way to peek inside a blackhole??)
An object that accelerates as it falls past the event horizon toward the singularity will cause gravity waves to propagate outward from the object at the speed of light. But those waves will never reach the horizon (or an outside observer) because everything leaving the object at any speed or direction will converge at the singularity; from its frame of reference the horizon only exists in the past. Anything that enters the horizon is no longer causally connected to the outside universe.
So how does mass falling into a blackhole ever appear to add to its mass at the centre? If we're saying even gravitational waves can't escape. This sounds like two merged blackholes don't actually ever merge, they get forever 'stuck' at each others event horizon.
If that were the case it feels like the rapid oscillation of gravitational waves that LIGO detected should actually slow down as the blackholes horizons touch. But as far as I've seen this isn't the case. The waves increase rapidly in frequency until there's an abrupt moment the blackholes merge and the waves abruptly stop?
But that makes no sense if each blackhole is progressively 'red shifted' at the others horizon
As a mass falls into a black hole, the radius of the event horizon increases, the black hole is pulled toward the mass enough to conserve their combined momentum, and their electric charge and angular momentum similarly combine. Those are the properties that change when a black hole merges with another black hole or any other infalling mass, and none of it depends on anything that happens inside the horizon.
And it’s true that events near the merging event horizon would appear to undergo time dilation to an outside observer, but I assume that rotational frame-dragging would balance out that effect on the gravitational waves produced (although the actual math is beyond me).
When blackholes merge there must be a period of time between the singularities crossing each others event horizon and the singularities actually merging. During this brief period they are still rotating each other and therefore still doing the thing that's generating gravitational waves.
What I'm trying to figure out whether LIGO is detecting any of these gravitational waves produced after the blackholes have crossed each others event horizon?
If they are then that's information being conveyed out of the blackhole by gravity.
If they are not then that suggests that we never really observe blackholes merge. And the movement of one round the other becomes unobservable at the point they reach each other's event horizon. But if this is the case then the blackholes merging must appear 'frozen' at the event horizon in much the same way light is?
Black holes (and their singularities) never cross each other’s event horizons—their event horizons just merge.
Maybe you’re imagining event horizons as being caused by the singularities inside them. That isn’t strictly true: when a star collapses into a black hole, the event horizon forms before the singularity does. And once the event horizon forms, nothing inside it (including the not-yet-formed singularity) is part of our universe any longer—as far as the outside universe is concerned, the event horizon itself is the black hole (and is its own cause).
Think of black holes merging like soap bubbles merging—it’s the surfaces themselves that merge, not anything inside that’s generating them.
Thanks that makes sense. I guess the consequence of that is that merged blackholes are "lumpy". As in there's an orientation of the two previous centres of mass frozen in time some distance from each other. Presumably if we were close enough we'd be able to detect if we're looking at the two singularities side on or in a line? The event horizon would be a sort of oblate 8 shape on its side?
Edit; forgot to add.. this doesn't sound like what we're hearing where LIGO has translated its signals into sound. That sounds like the ever increasing rate of the blackholes orbiting each other until there's an abrupt culmination and calm afterwards.