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??)
That will demand a direct observation to answer
To my completely unscientific gut instinct, the point at which movements of a singularity cease being detectable is when it gets to where the event horizon of the other blackhole was (prior to them starting the merge). Not that any of this makes any sense. But if the event horizon is where regular matter appears to freeze and red shift without ever seeming to cross. Then that is because light cannot escape the gravitational well. But then the same surely applies to gravitational waves travelling at the speed of light. They can’t escape the gravitational well either. So the last we can detect of a merging black hole is when its centre has approached to the same distance at which other matter appears to freeze too - at the event horizon.
So for two equally sized blackholes that would leave them about an event horizons width away from each other. My point being, that would surely be distinct enough to be observable. Would could at least tell if such a system were spinning because the gravitational profiles would change with each rotation.
Yeah… But the singularity is hypothetical, we don’t know if they exists. We know that blackholes exists, but how their inside’s are is a different topic. And things don’t just appear to be frozen when they approach the blackhole, they (from our perspectives) are frozen, they did not crossed it yet because of the time dilation.
For ‘singularity’ really I’m just referring to ‘mass at the centre of a blackhole’. It seems like this should behave like any other mass falling into a second blackhole. Ie frozen and ‘redshifted’ forever at the event horizon. Difference here being the first blackhole causes the event horizon to be around it too. It just doesn’t feel right that we’d be getting gravitational waves of two blackholes circling each other until they physically combine. That would be gravitational waves coming out of the event horizon somehow.
The waves come from the circling, not the merge itself.